Advantages And Disadvantages Of Virus Spreading

Advantages And Disadvantages Of Virus Spreading
The main aim of this research is to analyze different approaches to the problem of virus spreading and propose new methods which are based on the
comprehensive analysis of previous solutions. This paper outlines pros and cons of three models such as susceptible–infected–susceptible (SIS),
susceptible–infected–removed (SIR) and susceptible–inflected–removed–antidotal (SIRA). From this survey we could make a conclusion that all
existing models mentioned above are appropriate for computer network protection from the virus spreading problem. However, all these approaches
have a number of disadvantages. So, in terms of lack of safety in computers protection from virus spreading new solutions should be found.
Introduction
Background. In my final graduation work, which ... Show more content on Helpwriting.net ...
In previous works researchers have frequently used epidemiological models for modeling the dynamics of computer virus spreading. Nowadays there
are two main mathematical approaches, as described in [3]. The first one is deterministic model which is based on differential equations and is suited
for large networks, for instance, global Internet network. Another approach is stochastic model that employ Markov chains and diffusion processes.
This method suits better small local computer networks and in my work I will focused mainly on this approach. In words, Markov chain is the
sequence of random events with a finite or countable number of outcomes, characterized by the property that, for a fixed present the future does not
depend on the past. So, from the theoretical side, this approach will be the most suitable and urgent for modeling this kind of system, because all time
moments between different conditions of the system would be distributed with Poison distribution. That is why in my work I decided to use stochastic
model approach based on Markov
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Daily Water Level Forecasting At A Reservoir Using A...
Daily Water Level forecasting in a Reservoir using A Probabilistic Nonlinear Model
A reservoir is a place, either natural or artificial for storing water and this storage may be drawn from for use, often to meet the uneven distribution
of water in space and time. The natural flow of rivers and streams differ significantly with the change in weather throughout a year and may lead to
overflows (flood) or low flows (droughts) in various regions (Postel and Richter 2012; Poff et al. 2007). Under such conditions, water reservoirs
play an important role to alleviate these natural disasters by holding water during periods of floods, and allowing steady release of water during
periods of droughts. In addition, these are widely used as the source of water for drinking as well as irrigation. Therefore, accurate forecasts of
reservoir water level is highly essential for optimizing the various water management issues.
Concurrently, forecast of water–level in reservoirs is a very challenging task, since it is impacted by not only stream flow volume but also on other
factors such as flow velocity, stream flow path, rainfall, temperature, watershed characteristics, tributaries and the like (Bates et al. 2008; Piao et al.
2010; Chamoglou et al. 2014). Tributaries, that convey suspended sediment, severely shorten the reservoir life through siltation and rapidly reduce its
storage capacity (Panagopoulos et al. 2008). Water losses through evaporation may also occur in a reservoir (Christensen

A Paradigm For Multiple Input Multiple Output ( Mimo )...
Abstract– A paradigm for multiple–input multiple–output (MIMO) channel modeling demands diversity technique to compensate the effects of fading
and shadowing. In this paper, error performance of MIMO system is analyzed with orthogonal space time block code (OSTBC) and maximal ratio
combining (MRC) techniques over Weibull–gamma (WG) fading channel. WG distribution forms a composite channel model which is used to
determine the effects of multipath as well as shadowing. Closed form expressions for symbol error rate (SER) are computed for MIMO systems using
OSTBC and MRC in this scenario. Consequently, the effects of fading severity by varying shape parameters are also shown by simulation and
analytical results. Keywords– Multiple–input multiple–output (MIMO), orthogonal space time block code (OSTBC), maximal ratio combining (MRC),
Weibull–gamma (WG) fading, symbol error rate (SER). Introduction In the present wireless systems, the demand of proliferation of bandwidth for high
data rate and reliable communication requirement is increasing. Multiple–input multiple–output (MIMO) systems are investigated to achieve these
requirements. Also, diversity techniques are recommended to increase the reliability of system. Orthogonal space time block codes (OSTBCs) are
employed in MIMO systems to achieve the full transmit diversity while allowing a simple maximum likelihood decoding algorithm. This algorithm is
based on linear processing of received signals [1–2]. MIMO system uses

Performance Evaluation Of Ofdm System Using Non Linear...
PERFORMANCE EVALUATION OF PAPR REDUCTION IN OFDM SYSTEM USING NON LINEAR COMPANDING TRANSFORM
ABSTRACT
Orthogonal Frequency Division Multiplexing is considered as an advanced communication model which has wide range of applications such as 3G,
4G, and Wi–Fi etc. Though orthogonal frequency division multiplexing has lots of advantages over conventional communication models such as
FDMA, CDMA still it has some disadvantages in that the major drawback is Peak to Average Power Ratio. In literature several theories are
proposed to resolve this issue but none of the algorithm is designed to meet the practical approach. In our work a novel approach is present to resolve
the Peak to Average Ratio by introducing the variable slopes parameters K1, K2 and inflexion points A (A>0) and CA (0<C<1) in theprobability density
function in the Non Linear Companding Transform Technique then based on the inflexion point and variables parameter analysis, the
performances of two incompatible features PAPR and Bit Error rate can be achieved. Selection of Non Linear Companding transform parameters plays
an essential role as overall performance, robustness depends on it. The proposed theoretical work results can be view through MATLAB simulations.
OVERVIEW
Orthogonal frequency division multiplexing is considered as highly successful communication model compares to conventional communication models
because of low sensitivity to multipath propagation and eminent spectral efficiency. OFDM too

Questions On Faults And Degradation
section{Simple POdtSHS System Example} label{sec:shsexample} Since we are interested in faults and degradation, the system will have three modes
and one continuous state, i.e.: egin{itemize} item $mathcal{Q}={q_1,q_2,q_3}={mathrm{OK},mathrm{FAULTY},mathrm{BROKEN}}$ item
$n(q_1)=n(q_2)=n(q_3)=1$ end{itemize} The modes signalize the faults of the system, with $q_1$ being the faultless mode, $q_2$ denoting a fault in
the system that compromises its operation and finally $q_3$ denoting completely broken system that is incapable of operating at all. The continuous
state $x$ denotes the degradation level of the equipment and can have any value from interval $[0,100]$. The outputs will be observed degradation
level and observed mode. Thus the observation vector will be a two–element vector $y=(y_1,y_2)$ with $y_1in,[0,100]$ meaning an observed
(estimated) level of degradation, e.g. from computing some key performance indicator (KPI) from sensor measurements. The
$y_2in{mathrm{OK},mathrm{FAULTY},mathrm{BROKEN}}$ is again observed (or estimated) mode, e.g. from some fault detection engine in
place which itself aggregates and transforms sensor readings into this one discrete signal. The outputs are subject to sensor noise etc., so they do not
perfectly correlate with the true system state. The actions will depict the system maintenance and thus the action space $mathcal{U}$ will be a
three–element set ${u_1,u_2,u_3}$ with the first element meaning doing no maintenance action, the

MAT 540 MIDTERM EXAM Essay
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MAT 540 MIDTERM EXAM
1. Deterministic techniques assume that no uncertainty exists in model parameters.
2. A continuous random variable may assume only integer values within a given interval.
3. A joint probability is the probability that two or more events that are mutually exclusive can occur simultaneously.
4. A decision tree is a diagram consisting of circles decision nodes, square probability nodes, and branches.
5. A table of random numbers must be normally distributed and efficiently generated.
6. Starting conditions have no impact on the validity of a simulation model.
7. The Delphi develops a consensus forecast about what will occur in the future.
8. Qualitative methods are ... Show more content on Helpwriting.net ...
27. The drying rate in an industrial process is dependent on many factors and varies according to the following distribution. Compute the mean drying
time. Use two places after the decimal.
28. A loaf of bread is normally distributed with a mean of 22 oz and astandard deviation of 0.5 oz. What is the probability that a loaf is larger than 21
oz? Round your answer to four places after the decimal.
29. An investor is considering 4 different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions,
represented in the payoff table below.

Economic Condition
Poor Average Good Excellent
Investment (S1) (S2) (S3) (S4)
A 50 75 20 30
B 80 15 40 50
C –100 300 –50 10
D 25 25 25 25
If the probabilities of each economic condition are 0.5, 0.1, 0.35, and 0.05 respectively, what is the highest expected payoff?
30. The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with
how well taxpayers comply with the new tax code. The following payoff table is given in thousands of dollars (e.g. 50 = $50,000).
If he uses the maximin criterion, how many new workers will he hire?
31. Consider the following distribution and random numbers: If a simulation begins with the first random number, what would the first simulation
value would be __________.
32. Given the

Design And Development Of Simulator For Risk Analysis
Design and Development of Simulator for Risk Analysis Harpreet Kaur. Er. Isha Sharma PG Student Assistant Professor Deptt. Of Computer Science
and EngineeringDeptt. Of Computer Science and Engineering Chandigarh University, GharuanChandigarh University, Gharuan Abstract– In software
designing every phase consume some resources and some cost which is associated with these resources. In every case the cost of software is vary with
the development duration of the software. The most important work done by the project manager is to maintain the balance between time... Show more
content on Helpwriting.net ...
Booking a product task is greatly troublesome as the expected to finish an undertaking development movement is difficult to gauge. The achievement
of any venture is all that much ward upon the nature of planning, scheduling and controlling the different period of the undertaking. Program
Evaluation and Review Technique (PERT) is a guide to administration in assisting and controlling the assets to meet the calendar fruition date of the
activities which include the high level of instability.. Process recreation is a critical system to assess the effect of proposed changes in the process.
The discriminating way technique for booking a venture is a key device for task administration. A timetable system speak to the venture technique. it is
broadly acknowledged that venture calendar assumes a key part in task administration due to its impact on undertaking achievement. To consolidate
instability in planning procedure is to apply the discriminating way booking procedure and after that investigation the outcomes from a probabilistic
viewpoint Monte Carlo recreation is a variable device to give a numerical estimation of the stochastic highlight of the framework reaction.
TRADITIONAL PROBABILITY ANALYSIS METHOD Duration Risk means the likelihood and loss of in culmination in the aggregate specified
duration utmost. As per the meaning of span hazard, the numerical articulation of duration risk can be characterized as takes

What Is Offline And Online Scale Computation?
3.1 Offline and online scale computation For different values of Оє the multiscale basis changes as the pde solution changes. To address this issue
offline–online computation is used where in offline stage for representative values over a grid of Оє's the offline basis and the corresponding linear
space is constructed. The online basis then constructed solving a local problem for each candidate Оєв€
—, using the principal component direction of
the spectral problem. The mathematical details of the online–offline technique can be found in Guha and Tan (2016), Efendiev et al( 2011). For a set of
values Оє1,...,ОєN solving local eigen value problem to detect the dominant scale (inverse of the eigen value) a offline space is constructed with basis...
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In particular Оє в€
ј GP(K) and log(Оє(x)) = п°…Оѕ в€
љО» e (x), for x в€€ D where K is covariance kernel on D with iii п
їјeigen values О»i and
eigen vectors ei(x) and Оѕi в€
ј N(0,1). 13 The goal is to derive the posterior distribution of Оє's or equivalently Оѕi's given observation and the model.
Posterior for Оє The posterior for Оє can be written as О (Оє|Y ) = p(Y |Оє)ПЂ(Оє) where p(Y |K) is the likelihood of Y given Оє which is a normal
distribution for the above error distribution assumption around the solution K(u,Оє) from the pde. This posterior is not closed form and
Metropolis–Hastings MCMC sampling is needed to draw sample from Оє. The likelihood computation involves solving for Оє and this solution would
be calculated using basis function (multiscale basis for example). Using simple coarse scale basis function that has a bilinear form in the coarse
grid and zero outside the coarse region, gives a low resolution solution that can be used to filter out the bad proposal value in MCMC set up. 3.3
Multilevel sampling with residue information Selecting the additional basis with this model based distribution the randomized forward solution can
be incorporated into a multilevel MCMC methodology (Dodwell et al., 2014). Two level sampling is proposed for convenience but additional levels
can be used. Two level sampling are done on the coarse level and fine scale; in coarse scale using coarse scale basis and in the fine level using
multiscale basis.

Drought As A Recurring Extreme Climate Event
Drought as a recurring extreme climate event can be defined from various perspective, including meteorological, hydrological, agricultural and
socio–economic aspects. Materials and Methods Study area Iran has an area of 1,648,000 km2, is situated in the south–western part of Asia. The
climate is influenced by Iran 's location between the subtropical humidity of the eastern Mediterranean area, the subtropical aridity of the Arabian
desert areas and its topographical features like presence of the Zagros Chain and the Elburz Chain in the west and the north of this country
respectively, two large deserts (the Lut desert and the Kavir desert) in the central Plateau and intensive elevation variability (from в€’25 m in coastal
regions of the Caspian Sea to 5,600 m in central Elburz Chains) (Fig. 1). Because of its geographical location and topographical features, Iran has a
variable climate however arid and semi–arid climate cover the majority of this country. This climate characterized by long, hot, dry summers and short,
cool winters (Ganji 1968).The average annual precipitation in Iran is approximately 250 mm (Moradi, 2004). The major exceptions are the higher
mountain valleys of the Zagros and the Caspian coastal plain, where precipitation averages at least 500 mm annually. In the western part of the Caspian,
annual precipitation exceeds 1,000 mm and is distributed relatively evenly throughout the year. This contrasts with some basins of the Central Plateau
of Iran that

Case Study Of Monte Carlo Simulation
Mental disorder can be classified into 4 categories: depression, bipolar affective disorder, schizophrenia and other psychoses and dementia.
According to World Health Organization, depression is one of the most common mental disorders worldwide. Globally, about 400 million people of
all ages suffer from depression. More women are affected than men. (WHO, Mental disorders, 2014) In Malaysia, some national surveys were
conducted in community households by trained medical professionals. According to the survey, a mental health problem in year 1996 was 10.7%.
(The Second National Health and Morbidity Survey (NHMS II) 1996, 1996) It had increased from to 11.2% in year 2006. (The Third National Health
and Morbidity Survey NHMS III 2006, 2008) In... Show more content on Helpwriting.net ...
It shows all possible outcome and of decisions and assess the impact of risk and allows for better decision making under uncertainty. The technique
is used by professionals in such widely disparate fields including operational research, finance, insurance, medicine and engineering. Monte Carlo
simulation is used to solve both probabilistic and deterministic problems. In the case of a probabilistic problem a simple Monte Carlo approach can
be used to observe the random numbers, which is chosen in such a way that they directly simulate the physical random processes of the original
problem, and to assume the preferred solution from the behavior of these random numbers. Monte Carlo simulation has wide application in performing
risk analysis by building models of possible results by substituting a probability distribution for any factor that has inherent uncertainty. It then
calculates results by using a different set of random values over and over from the probability functions. Monte Carlo simulation produces probability
distributions of possible outcome values. Different outcome occurred can lead to different probabilities of variables. Probability distributions are a
realistic way of describing uncertainty in variables of a risk analysis. (James, T., Reeve,T., Nasiri,

A Unified Probabilistic Generative Model
To model user check–in activities, we propose a unified probabilistic generative model TRM to sim– ulate the process of user's decision–making for
the selection of POIs. Figure 1 shows the graphical representation of TRM where N, K and R denote the number of users, topics and regions, re–
spectively. We first introduce the notations of ourmodel and list them in Table II. Our input data,
i.e., users' check–in records, are modeled as observed random variables, shown as shaded circles in
Figure 1. As a POI has both semantic and geographical attributes, we introduce two latent random variables, topic z and region r, which are responsible
for generating them, respectively. Based on the two latent factors, TRM aims to model and infer users' ... Show more content on Helpwriting.net ...
Thus, each topic z in TRM is not only associated with a word distribution П•z, but also with a distribu– tion over time П€z. This design enables П•z
and П€z to be mutually influenced and enhanced during the topic discovery process, facilitating the clustering of the words of POIs with similar
temporal patterns into the same topic with high probability. To integrate the check–in time information to the topic discovery process, we employ the
widely adopted discretization method in [Gao et al. 2013;
Yuan et al. 2013] to split a day into hourly–based slots.
In the standard topic models [Blei et al. 2003; Wallach et al. 2009], a document (i.e., a bag of words) contains a mixture of topics, represented by a
topic distribution, and each word has a hidden topic label. While this is a reasonable assumption for long documents, for short document Wv, it is most
likely to be about a single topic. We therefore assign a single topic to the document Wv.
Similar idea of assigning a single topic to a twitter post has been used before [Zhao et al. 2011].
User Mobility Modeling. Different from users' online behaviors in the virtual world, users' check–in activities in the physical world are limited by
travel distance. So, it is also importan– t to capture users' spatial patterns (or activity ranges) according to the location distributions of their historical
checked–in POIs. The spatial clustering phenomenon indicates that users are most likely to check–in a number

Statistics for Business and economics 10e homework...
Please complete the following problems in a Word document. Each problem is worth 3 points.
Chapter 4: 12, 14, 40
Chapter 5: 10, 22, 28
Chapter 6: 6, 16, 20, 24
Chapter 4
12. The Powerball lottery is played twice each week in 28 states, the Virgin Islands, and the District of Columbia. To play Powerball a participant
must purchase a ticket and then select five numbers from the digits 1 through 55 and a Powerball number from the digits 1 through 42. To determine
the winning numbers for each game, lottery officials draw five white balls out of a drum with 55 white balls, and one red ball out of a drum with 42
red balls. To win the jackpot, a participant's numbers must match the numbers on the five white balls in any order and the number ... Show more content
on Helpwriting.net ...
Assume that each unit demanded generates $70 in revenue and that each unit ordered costs $50. How much will the company gain or lose in a month
if it places an order based on your answer to part (a) and the actual demand for the item is 300 units?
The loss would be $1,250
28. A Harris Interactive survey for InterContinental Hotels & Resorts asked respondents, "When traveling internationally, do you generally venture out
on your own to experience culture, or stick with your tour group and itineraries?" The survey found that 23% of the respondents stick with their tour
group (USA Today, January 21, 2004).
a. In a sample of six international travelers, what is the probability that two will stick with their tour group?
b. In a sample of six international travelers, what is the probability that at least two will stick with their tour group?
c. In a sample of 10 international travelers, what is the probability that none will stick with the tour group?
Chapter 6
6. The label on a bottle of liquid detergent shows the contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according

to the following probability density function.
a. What is the probability that a bottle will be filled with between 12 and 12.05 ounces?
b. What is the probability that a bottle will be filled with 12.02 or more ounces?
c. Quality control accepts a bottle that is filled to

Hlt 362v Workbook Exercise 18
1. In comparing men and women, which group had higher body image scores? Provide a rationale for your answer. Women had higher body image
scores with a X_пЂЅпЂ 73.07 compared to men with a X_пЂЅпЂ 60.22. With this study, the higher the mean, the greater the body image scores. Thus,
the higher mean for women's body image scores showed that women have stronger body image scores than men. 2. Men had higher variability in
weight change over the last 12 months when compared to women. Is this statement true or false? Provide a rationale for your answer. True. SD
indicates variability or spread of scores. Men had higher variability in scores with a SD пЂЅпЂ 22.40 versus women with a SD пЂЅпЂ 13.63. This
shows that women had less variation in their... Show more content on Helpwriting.net ...
Round your answer to two decimal places. Assuming that the distribution of female body image scores is normal, 99% of the women's scores fall
between (29.39, 116.75). Calculation: X_п‚±пЂ 2.58(SD) X_пЂЅпЂ 73.07 SD пЂЅпЂ 16.93 73.07 в€’п
Ђ 2.58(16.93) пЂЅпЂ 73.07 в€’п
Ђ 43.68
пЂЅпЂ 29.39 73.07 пЂ«пЂ 2.58 (16.93) пЂЅпЂ 73.07 пЂ«пЂ 43.68 пЂЅпЂ 116.75 Expressed as (29.39, 116.75) 7. Assuming that the distribution is
a normal curve, 99% of men were between what ages? Round your answer to two decimal places. Assuming that the distribution of men's ages in the
sample is normal, 99% of the men were between the ages (21.04, 63.36). Calculation: X_п‚±пЂ 2.58 (SD) X_пЂЅпЂ 42.2 SD пЂЅпЂ 8.2 42.2
в€’п
Ђ 2.58(8.2) пЂЅпЂ 42.2 в€’п
Ђ 21.16 пЂЅпЂ 21.04 42.2 пЂ«пЂ 2.58(8.2) = 42.2 пЂ«пЂ 21.16 пЂЅпЂ 63.36 Expressed as (21.04, 63.36) 8.
Assuming that the distribution is a normal curve, 95% of men were between what ages? Round your answer to two decimal places. Assuming that the
distribution of men's ages in the sample is normal, 95% of the men were between the ages (26.13, 58.27). Calculation: X_п‚±пЂ 1.96 (SD) X_
пЂЅпЂ 42.2 SD пЂЅпЂ 8.2 42.2 в€’п
Ђ 1.96(8.2) пЂЅпЂ 42.2 в€’п
Ђ 16.07 пЂЅпЂ 26.13 42.2 пЂ«пЂ 2.58(8.2) пЂЅпЂ 42.2 пЂ«пЂ 16.07
пЂЅпЂ 58.27 Expressed as (26.13, 58.27) 9. Did HIV–positive participants have signifi cantly higher body image scores than those with AIDS?
Provide a rationale for your response. No. It shows in the Study Results, HIV–positive participants' mean score for body image was 68 compared to
60.5 for those with AIDS. These two groups were

Advantages And Disadvantages Of Distribution-Free Control...
We present an overview of literature on nonparametric or distribution–free control charts for uni–variate variable data. We highlight various advantages
of these charts while pointing out some of the disadvantages of the more traditional, distribution based control charts. Specific observations are made
in the course of review of articles and constructive criticism is offered so that opportunities for further research can be identified. Connections to some
areas of active research are made, such as sequential analysis, which are relevant to process control. We hope that this article leads to a wider
acceptance of distribution– free control charts among practitioners and serves as an impetus to future research and development in this area.... Show
more content on Helpwriting.net ...
Clearly, the quicker the detection and the signal, the more efficient the chart is. The number of samples or subgroups that need to be collected before
the first out of–control signal is given by a chart is a random variable called the ran length. The efficiency of a CC depends on the probability
distribution of the run length. The most common efficiency criterion is to consider the average run length (ARL), which is the expected value of the
run length distribution. It is desirable (often stipulated) that the ARL of a chart be large when the process is in–control and small when the process is
out–of control. The false alarm rate is the probability that a chart signals a process change when in fact there is no change, that is, when the process is
in–control. This is similar to the probability of a Type I error in the context of hypothesis testing. In practice, the stability of a process is usually
determined relative to one or more of its output characteristics such as the mean and/or the variance. Two control charts are often compared on the
basis of out–of–control ARL, such that their respective in–control ARL's are roughly the same. This parallels comparing two statistical tests on the
basis of power against some alternative hypothesis when they are roughly of the same

Producing Dat Designing Samples
Producing Data : в—Џ Designing Samples : To design a sample one is looking into a population which is defined as the entire group of individuals
that we are using to gather information from. Within this population we are looking for a sample, which is the random information we gather to
observe from the population. The population is chosen based on what information we are trying to gather, you can gather information from
populations by using a census or sampling methods. When sampling you are studying part of a population to gather information about it as a whole,
while a census makes effort to get information from every individual in the population. There are various ways to create a sample, both right and
wrong, an example of a wrong way... Show more content on Helpwriting.net ...
Inference : в—Џ Estimating Confidence : When estimating the accuracy within the guess of your experiment, you do so by using your margin of
error which is showing how accurate you believe your guess is. A confidence interval equals to your estimate plus or minus your margin of error. в
—Џ
Inference for Regression : Statistical inference can bring us to conclusions about a population through the looking of sample date and probability to
show us how reliable our inferences are. Our confidence interval will more times than not tell us what would occur if specific intervals were to occur,
the larger the confidence interval the more likely the estimate is to be true. While a determined P value shows us how unlikely the observed outcome
is. With these assumptions we can come to a null hypothesis which states that there is no significant difference Probability: в—Џ Probability Models :
There are various ways of determining probability outcomes by usually, listing your possible outcomes and determining your probability of each
outcome. A probability model is a description of a random phenomenon that is made up of two parts. One probability model is through sample space
S of a random phenomenon is a set showing all possible outcomes, which came become very easy or extremely difficult due to what type of

Math Midterm Essay
Deterministic techniques assume that no uncertain exists in model parameters.
A: True
An inspector correctly identifies 90% of the time. For the next 10 products, the probability that he makes fewer than 2 incorrect inspections is .736.
A: Use Binomial table to discover , add 3 probabilities for 0,1,2
A continuous random variable may assume only integer values within a given interval.
A: False
A decision tree is a diagram consisting of circles decision nodes, square probability nodes and branches.
A: False
A table of random numbers must be normally distributed and efficiently generated
A: False
Simulation results will always equal analytical results if 30 trials of the simulation have been conducted.
A: False
Data cannot ... Show more content on Helpwriting.net ...
A: .01
Coefficient of determination is the percentage of the variation in the _ variable that results from the _ variable.
A: Dependent/independent
In exponential smoothing the closer alpha is to _ the greater the reaction to the most recent demand.
A:
_ is a linear regression model relating demand to time.
A: linear trend
_ is a measure of the strength of the relationship between independent and dependent variables.
A: Double check definition possibly coefficient of determination or correlation
Consider the following graph of sales: which of the following characteristics is exhibited by the data:
A: trend plus seasonal
Which of the follow characteristics is exhibited by the data
A: None of the above
_ is the difference between the forecast and actual demand

A: forecast error
Given the following data on number of pints of ice cream sold at a local ice cream store for a 6 month period time frame:
If the forecast for period 5 is equal to 275 use exponential smoothing a to compute a forecast period 7.
THe Drying rate in an industrial process is dependent on many factors and varies according to the following distribution.
Compute the drying time. Use two places after the decimal.
A: takes values of variable and multiply with the relative frequency then add them up to get answer.
Life insurance company .... With a mean of 68 years and a standard deviation of 4 years. What proportion of the plan recipients would receive
payments beyond age 75?

Information About Reliability And Maintainability...
ABSTRACT: The core aim of preparing this report is to gather information from numerous sources in reliability and maintainability management field.
However, this report consists of five main chapters that cover general information about reliability and maintainability management. In chapter one,
different definitions and terms have been listed in details to familiarize the reader with the topic. In addition, there is a section that is specified to
clarify the needing for reliability and maintainability in plants. Due to the confusion that might happen among people about the differences between
reliability and maintainability management, these differences have been explained briefly in chapter one. In chapter two and chapter five, several
helpful mathematical equations in reliability and maintainability management have been mentioned briefly and in attractive way. The reason to address
these equations is to clarify the different relations and functions that are used commonly in reliability and maintainability world. In these chapters,
some figures and charts have been used to simplify mathematics in reliability and maintainability management field. In chapter four, the principle of
maintainability management has been explained in details. Furthermore, this chapter has highlighted the function and organization of maintenance
departments and how it is usually being organized. Also this chapter has explained the elements that lead to an effective maintenance management.

The Classical Expected Utility Theory And The Dual Theory...
INTRODUCTION:
Identifying, defining risks (market risks as well as non–market risks), presenting and justifying a unified framework for the analysis, construction and
implementation of risk measures are important components of insurance pricing.
According to the Oxford's advanced learners dictionary, risk can be defined as the possibility that something uncertain (not predictable) and unpleasant
will happen. Both financial and insurance organisations are therefore faced with this concept of risk in their everyday activities. Financial risk can be
said to be the possibility that the return achieved on an investment will be different from that expected, and also takes into account the size of the
difference. Whereas insurers will define risk as a chance of harm, damage or loss against something which is insured.
Several literatures reveal a good number of different approaches and theories to the price of risk. The two main competing economic theories we shall
consider are the classical expected utility theory, and the dual theory of risk which was developed by Yaari(1987).
They defined the price of an insurance risk excluding other expenses as the risk adjusted premium.
The rest of this paper is structured as follows: section 2 presents the class of distortion operators used in insurance pricing, their properties and an
application of pricing by distortion. Section 3 incorporates a new pricing principle by Wang (2002) and its relevance to natural hedging.
Section 4

Probability Modeling And Statistics Essay
Project On Probability Modeling & Statistics.
Topic : Binomial Poisson and Normal.
Please mention The Measures of central tendency
The use of these distributions (in which cases these distributions are used) with illustrations.
Binomial approximation to the normal distribution.
What is Skewness and Kurtosis? How it is used and interpreted?
Binomial Distribution :
This kind of distribution is applied to single variable discrete data where results are the number of "successful outcomes" in a given scenario.
E.g. :
no. of times the lights are red in 20 sets of traffic lights,
No of students with green eyes in class of 40,
No. of plants with diseased leaves from a sample of 50 plants.
Binomial distribution is used to calculate the ... Show more content on Helpwriting.net ...
Normal Distribution:
The normal distribution is a very common continuous probability distribution. Normal distribution is important in statistics and is often used in the
natural and social sciences to represent real–valued random variables whose distributions are not known.
This distribution is useful because of the central limit theory. In its most general form, under some conditions which include finite variance), it states
that average of random variables independently drawn from independent distributions converge in distribution to the normal, that is, become normally
distributed when the number of random variables is sufficiently large.
The normal distribution is sometimes informally called the bell curve. However, many other distributors are bell–shaped( such as the Cauchy, students
and logistic distribution).
Measure of Central Tendency :
The Mean, Median and Mode are all valid measures of central tendency, but under different conditions, some measures of central tendency become
more appropriate to use than others.
Mean

The Mean is essentially a model of your data set. It is the value that is the most common. However, Mean is not often one of the actual values that
you have observed in your data set, but it has one of its important properties is that it maximizes error in the prediction of any one value in your data
set. That is, it is the value that produces the lowest amount of error

Safety and Reliability Engineering Past Paper
EG40JQ/12
UNIVERSITY OF ABERDEEN
SESSION 2011 – 2012
Degree Examination in EG40JQ SAFETY AND RELIABILITY ENGINEERING
Friday 20 January 2012
Notes: (i)
(ii)
2.00 p.m. – 5.00 p.m.
Candidates ARE permitted to use an approved calculator
Data sheets are attached to the paper.
Candidates should attempt all FIVE questions.
REGULATIONS:
(i)
You must not have in your possession any material other than that expressly permitted in the rules appropriate to this examination. Where this is
permitted, such material must not be amended, annotated or modified in any way.
(ii)
You must not have in your possession any material that could be determined as giving you an advantage in the examination.

(iii)
You must ... Show more content on Helpwriting.net ...
It is given that t = 6.25mm.
Basic
variable Пѓy D
Mean
Coefficient of variation 240 MPa 0.11
225 mm 0.004
[6 marks]
Qu. 3 continued overleaf/
3/7
EG40JQ/12
Qu. 3 continued/
c)
A projectile of mass M is flying at a velocity V following a minor gas explosion o n an offshore installation. Write down the safety margin
corresponding to an event that the Kinetic Energy (KE = 0.5MV2 ) of the projectile is greater than 22500 J. Using an appropriate FORM approach,
determine the reliability index corresponding to this safety margin and comment on the sensitivity of the variables (limit your calculations to 2
iterations). Assume that the variables are statistically independent and normally distributed with the following parameters.
Basic variable
M
V
Mean
12 kg
59 m/s
Standard deviation
0.12 kg

2.95 m/s
[11 marks]
Question 4.
A tank containing gasoline is surrounded by a circular dike of diameter 10 m. The gasoline leak s and occupies the area bounded by the dike. If there
is ignition, calculate:
(a) The total radiative flux from the flame. Use the following correlation for the geometry of the flame: H/D = 42{m'/[ пЃіaпѓ–(gD)]} 0.61 where H =
height of the flame (m), d = diameter of the pool of liquid (m), m' = mass transfer rate from pool to flame (kg s–1), пЃіa = density of air = 1.17 kg m–3
and g = acceleration due to gravity =
9.8 m s–2. Make

Statistics Assignment
Week 4 Exercises
Chapter 5 – Section 1. Question 5
To perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one or two separate steps,
and the second procedure requires either one, two, or three steps.
a. List the experimental outcomes associated with performing the blood analysis.
Answer: There are two procedures that a lab technician must perform. The first procedure requires either one or two separate steps, which could be
named as x1 and x2. The second procedure requires either one, two or three steps, which could be named as y1, y2 and y3. The experimental
outcomes associated with performing the blood analysis from 1st procedure (x1,x2) and 2nd procedure: (y1,y2,y3): ... Show more content on
Helpwriting.net ...
What is the probability that it takes at least two sessions to gain the patient's trust?
Answer: The probability that is takes at least two sessions to gain the patient's trust is 0.83, because
Probability xв‰Ґ2=f2+f3=26+36=0.8333=0.83
Chapter 5 – Section 3. Question 17
a. Let x be a random variable indicating the number of times a student takes the SAT. Show the probability distribution for this random variable.
Answer: The probability distribution: Number of Times (x)| Number of Students| f(x)| 1| 721,769| 0.4752| 2| 601,325| 0.3959| 3| 166,736| 0.1098| 4|
22,299| 0.0147| 5| 6,730| 0.0044| | 1,518,859| 1.0000|
b. What is the probability that a student takes the SAT more than one time?
Answer: The probability that a student takes the SAT more then one time is 0.5248, because
Probabilityx>1=f2+f3+f4+f5=0.3959+0.1098+0.0147+0.0044=0.5248
c. What is the probability that a student takes the SAT three or more times?
Answer: The probability that a student takes the SAT three or more times is 0.1289, because
Probabilityxв‰Ґ3=f3+f4+f5=0.1098+0.0147+0.0044=0.1289
d. What is the expected value of the number of times the SAT is taken? What is your interpretation of the expected value?
Answer: The expected value of the number of times the SAT is taken is 1.6772, because
Ex=Ој=ОЈxfx
x| f(x)| xf(x)| 1| 0.4752| 0.4752| 2| 0.3959| 0.7918| 3| 0.1098| 0.3293| 4| 0.0147|

The Problem Of Providing Coverage Using A Group Of Mobile...
The problem of providing coverage using a group of mobile agents is investigated, where it is desired to minimize the overall coverage metric (service
cost) while achieving maximum coverage with minimum actuator energy required by each agent. In addition, a distributed multi–agent area coverage
control (MAACC) law is then provided which guarantees the convergence of agents to the optimal configuration with respect to the cost (coverage
metric) function. A common assumption in all of the coverage control results is that the distribution of sensory information in the environment is
known apriori by all agents. The proposed cooperative area coverage control framework is based on two interdependent tasks: (i) online learning
of the coverage area and storing of the data in the form of a "probability map"; and (ii) utilization of the probability map (which is used as a search
map) and other data collected to compute online a positional error trajectory (e(t)) for the agents to follow at specified sampling time steps. The group
of agents is considered as being a group of autonomous agents which exchange data but ultimately make their own decisions based on the received
data collected during an area coverage mission. In addition to the probability map, each agent in a multi–agent system transmits its position information
to its neighbours and receives the same information from them. The agents possess the probability maps (made possible via time–varying density
function) of targets

A Analysis On Probabilistic Risk
. Risk AnalysisEquation Chapter 5 Section 1 Probabilistic risk analysis is becoming more and more important in long–term damage estimation for
structure. In 2010, American Society of Civil Engineering (ASCE) defines Risk–Targeted Maximum Considered Earthquake ground motion maps for
the United States by explicitly targeting a probabilistic 1% risk of collapse in 50 years. Risk analysis is used to combine with earthquake–caused
death, downtime and repair cost to estimate seismic performance of bridges and other structures. For instance, according to [Bazzurro et al,2006],
post–main–shock risk is used to make a decision of repairing a building by calculating the probability that aftershock ground motion (demand) will
exceed the structural capacity. The goal of this chapter is introducing a method to compute the probabilistic seismic risk for both main–shock and
aftershock. Then we can use this to assess risk of specific structure in practice. The core of probabilistic seismic risk analysis includes two parts:
couples (1) ground motion hazard analysis for the site of interest; (2) the fragility analysis of the structure (located on that site) with respect to potential
ground motion intensities. These two parts have been introduced in last few chapters, so the next step is to combine all information about demand and
capacity of the structure to compute the final risk results. 5.1. Main–shock Risk When the damage state is the

Model And Assumptions Of The Royle Nichols Model
Model and Assumptions The Royle–Nichols model allows estimation of abundance from multiple observations of present–absent animals without
specifically marking the animal. This model represents the spatial distribution of the species observed. Several assumptions are made but two of them
are fundamental for this model. First one is that the spatial distribution of the animals across survey sites follows Poisson distribution, and second is
the probability of detecting an animal at a site is a function of how many animals are actually at that site. The Poisson distribution represents the
mechanism of spatial distribution which is simply how many animals occur at each site within the study area. This model assumes that each site is
home to a certain number of species and this number does not change overtime, which means no deaths, births, immigration or emigration of the
observed species. The Poisson distribution has as the mean parameter О» ("lambda") which is the mean abundance across the observed sites.
The probability density formula of for Poisson distribution is F(x)= (e^– О»)* (О»^x)/ x! Where x is the number of animals at a given site and F(x) is
the generic term of any probability distribution. Given this information we can find the probability that a specific number of animals occupy a given
site. The graph for this formula takes different shapes. For example, if we calculate this function for О»=3 and x=5 animals, the result is a probability
of 0.10. The graph

News Vendor Model Explanation
Newsvendor Model
Chapter 9
1 utdallas.edu/~metin Learning Goals
пЃµ Determine
the optimal level of product availability
– Demand forecasting – Profit maximization
пЃµ Other
measures such as a fill rate
utdallas.edu/~metin
2
OвЂџNeillвЂџs Hammer 3/2 wetsuit
utdallas.edu/~metin
3
Hammer 3/2 timeline and economics
Generate forecast of demand and submit an order to TEC
Economics:

Each suit sells for p = $180 TEC charges c = $110/suit Discounted suits sell for v = $90
Spring selling season
Nov Dec Jan
Feb Mar Apr May Jun
Jul Aug
Receive order from TEC at the end of the month
пЃµ
Left over units are discounted
The "too much/too little problem":
– Order too much and inventory is left ... Show more content on Helpwriting.net ...
– Prob{demand is Q or lower} = Prob{the outcome of a standard normal is z or lower}, where
zпЂЅ
QпЂm
s
or Q пЂЅ m пЂ« z п‚ґ s
– (The above are two ways to write the same equation, the first allows you to calculate z from Q and the second lets you calculate Q from z.) – Look
up Prob{the outcome of a standard normal is z or lower} in the Standard Normal Distribution Function Table. utdallas.edu/~metin
10
Using historical A/F ratios to choose a Normal distribution for the demand forecast
пЃµ Start

with an initial forecast generated from hunches, guesses, etc.
– OвЂџNeillвЂџs initial forecast for the Hammer 3/2 = 3200 units.
пЃµ Evaluate
the A/F ratios of the historical data:
A/F ratio пЂЅ Actual demand Forecast
пЃµ Set
the mean of the normal distribution to
Expected actual demand пЂЅ Expected A/F ratio п‚ґ Forecast
пЃµ Set
the standard deviation of the normal distribution to
Standard deviation of actual demand пЂЅ Standard deviation of A/F ratios п‚ґ Forecast
11
utdallas.edu/~metin
OвЂџNeillвЂџs Hammer 3/2 normal distribution forecast
Product description JR ZEN FL 3/2 EPIC 5/3 W/HD JR ZEN 3/2 WMS ZEN–ZIP 4/3 Forecast Actual demand 90 140 120 83 140 143 170 156 Error
–50 37 –3 14 1995 521 2817 A/F Ratio 1.5556 0.6917 1.0214 0.9176
...
ZEN 3/2 ZEN–ZIP 4/3 WMS HAMMER 3/2 FULL Average Standard deviation
...
3190 3810 6490
... ...
1195 3289 3673
...

0.3746 0.8633 0.5659 0.9975 0.3690
Expected actual demand пЂЅ 0.9975 п‚ґ 3200 пЂЅ

Automatic Surveillance: Vision Detection Using Gaussian...
Automatic surveillance application has been a subject of extensive research during last decades to develop robust application. As one of its important
application, the vision detection and localization interest in detecting moving objects under the challenging conditions of the illumination change,
occlusion, shadow and perturbation of the images sources. In vision detection system, the techniques used are either background subtraction based or
feature detection based. The background subtraction based techniques interests in detecting variation within the scene across several image frames.
This approach is based on comparing the current image with a reference one(s) of the background. Pixels of sharp variations are consequently classified
... Show more content on Helpwriting.net ...
Another technique is the Eigen backgrounds [6], this approach is based on an eigenvalue decomposition which is applied to the whole image. This
extended spatial domain enabled the exploration of the spatial correlation and avoiding the tiling effect of block partitioning. The method has two
phases that alternate with a learning phase for samples acquisition and eigenvector matrix computation and followed by classification step for
foreground detection. The Gaussian process presented in [7] , is a non parametric tool that performs Bayesian inference, is gaining great respect of the
research community, and thought most of the investigation in this domain is focused on its theory, great efforts consider interpreting this theory to real
application. In the same reference, the binary Gaussian process classifier is proposed as foundation of Gaussian process classiп¬Ѓcation. While in [8],
Laplace approximation as a tool of inference in Gaussian process models was suggested as a tool supporting the Gaussian binary classifier. The
generalization from two–class classification using binary Gaussian classifier to multiclass classification was proposed in [9], in this approach, a
technique of voting and combinations of approximate posterior probabilities is used to achieve simple

A Review On Thing Net Works
In numerous genuine applications, other than the input and thing content data, there may exist relations (or systems) among the things which can
likewise be useful for proposal. For instance, in the event that we need to prescribe papers (references) to clients in Cite ULike, the reference relations
between papers are useful for suggesting papers with comparable subjects. Different case of thing net–works can be found in hyperlinks among site
pages, motion pictures coordinated by the same executives, et cetera. In this paper, we build up a novel progressive Bayesian model, called Relational
Collaborative Topic Regression (RCTR), to join thing relations for suggestion. The principle commitments of RCTR are laid out.
II. Foundation: In this area, we give a brief presentation about the back–ground of RCTR, including CF based suggestion, network factorization (MF)
(likewise called inactive component model) based CF strategies and CTR. A.CF Based Recommendation Collaborative theme relapse is proposed to
prescribe records (papers) to clients via flawlessly incorporating both input framework and thing (archive) content data into the same model, which can
address the issues confronted by MF based CF. By joining MF and inactive Dirichlet distribution (LDA), CTR accomplishes preferable expectation
execution over MF based CF with better interpretable results. In addition, with the thing content data, CTR can anticipate input for out–of–grid things.
The graphical model of CTR is

A & M Research Statement
Research Statement
Nilabja Guha Texas A&M University
My current research at Texas A&M University is in a broad area of uncertainty quantification (UQ), with applications to inverse problems, transport
based filtering, graphical models and online learning. My research projects are motivated by many real–world problems in engineering and life
sciences. I have collaborated with researchers in engineering and bio–sciences on developing rigorous uncertainty quantification methods within
Bayesian framework for computationally intensive problems. Through developing scalable and multi–level Bayesian methodology, I have worked on
estimating heterogeneous spatial fields (e.g., subsurface properties) with multiple scales in dynamical systems. In ... Show more content on
Helpwriting.net ...
Some of the areas I have explored in my Ph.D. work include measurement error model with application in small area estimation, risk analysis of
dose–response curves. The stochastic approximation methods have application in density estimation, deconvolution and posterior computation. A
discussion of my current and earlier projects are given next.
1 UQ for estimating heterogeneous fields
To predict the behavior of a physical system governed by a complex mathematical model depends on un– derlying model parameters. For example,
predicting the contaminant transport or oil production strongly influenced by subsurface properties, such as permeability, porosity and other spatial
fields. These spatial fields are highly heterogeneous and vary over a rich hierarchy of scales, which makes the forward models
1
be computationally intensive. The quantities determining the system are partially known and represent information at some range of spatio–temporal
scales. Bayesian modeling is important in quantifying the un– certainty, identifying dominant scales and features, and learning the system. Bayesian
methodology provides a natural framework for such problems with specifying prior distribution on the unknown and the likelihood equation. Solution
procedure use Markov Chain Monte Carlo (MCMC) or related methodology, where, for each of the proposed parameter value, we solve

Recent Work On Follow The Perturbed Leader ( Ftpl )...
Recent work on follow the perturbed leader (FTPL) algorithms for adversarial multi–armed bandit problem has highlighted the role of the hazard rate
of the distribution generating the perturbations.
Assuming that the hazard rate is bounded allows one to provide regret analyses for a variety of
FTPL algorithms for the multi–armed bandit problem. This paper pushes the inquiry into regret bounds for FTPL algorithms beyond the bounded
hazard rate condition. There are good reasons to do so: natural distributions such as the uniform and Gaussian violate the condition. We give regret
bounds for both bounded support and unbounded support distributions without assuming the hazard rate condition. We also disprove a conjecture that
the Gaussian ... Show more content on Helpwriting.net ...
The former corresponds to infimal convolution smoothing and the latter corresponds to stochastic (or integral convolution) smoothing (Abernethy et
al., 2014). Having a generic framework for understanding perturbations allows one to study a wide variety of online linear optimization games and a
number of interesting perturbations.
There has also been some work on understanding perturbation approaches in bandit problems.
Kujala and Elomaa (2005) and Poland (2005) both showed that using the exponential (actually double exponential/Laplace) distribution in an FTPL
algorithm coupled with standard unbiased estimation techniques yields near–optimal O(NT logN) regret in T rounds with N arms. Unbiased estimation
needs access to arm probabilities that are not explicitly available when using an FTPL algorithm. Neu and BartВґok (2013) introduced the geometric
resampling scheme to approximate these probabilities while still guaranteeing low regret. Recently, Abernethy et al. (2015) analyzed FTPL for
adversarial multi–armed bandits and provided regret bounds under the condition that the hazard rate of the perturbation distribution is bounded. This
condition allowed them to consider a variety of perturbation distributions beyond the exponential, such as gamma, Gumbel, Frechet, Pareto, and
Weibull.
Unfortunately, the bounded hazard rate condition is violated by two of the most widely known distributions: namely the uniform1 and the Gaussian
distributions. As a result, the

Statistical Methods in Measuring Corporate Performance
The purpose of this paper is to provide an overview of commonly used statistical data in the measurement of corporate performance by examining
various models and methods.
Corporate performance can be defined as fundamental measures of organizational aptitude used to assess the "health" of the organization and to
provide focused direction to operations while supporting managers. In order to measure the company's intangible assets such as customer relationships,
internal processes, and employee learning and development while aligning the corporation's overall business strategy, statistical analysis of
performance measurement data must be utilized.
The task of evaluating the latest performance measures and aligning business strategy ... Show more content on Helpwriting.net ...
Each is a reaction to the findings of the one before until a pattern can be observed. This is also rarely used in performance measurement.
Probability Distributions
Range and distributions depend upon the amount of data available. The information sought in performance measurement is usually continuous, that is,
measurable – and therefore denoted as f(x). Since the probability or distribution of possible probabilities is continuous, the likelihood that the
probability is any specific point estimate is really zero. The range for probability then depends on the level of valid, available information.
A probability distribution indicates all values that a random variable can assume and shows the likelihood of occurrence. By examining distributions of
data, important characteristics such as shape, location, variability, and unusual values can be detected. The conclusion as to the relationships between
different variables can then be generated from the observation of patterns in data.
An example of a normal distribution test is the Gauss curve. The bell shaped curve represents the odds of each outcome on the range of several
outcomes. In a normal distribution observations are distributed symmetrically around the mean, 68% of all values under the curve lie within one
standard deviation of the mean and 95% lie within two standard deviations3. This is good for intervallic continuous variables.
Another type of distribution is done when the results are not ranged along a

Decision Tree Case Study
Decision tree analysis
Decision tree analysis known as an analytical tool applied to decision–making under condition of uncertainty, also clarifying where there are many
possible outcomes for various alternatives and some outcomes are dependent on previous outcomes. However, decision tree will present as a diagram
by showing the relationship among possible courses of action, possible events and the potential outcomes for each course of action in the decision
(Drury, 2012). So decision tree analysis is useful for merchant navy company to understand in what direction their chance events are and what their
values in terms of profits and losses are for each of the two tooling alternatives, also visualize the outcomes of different prospects ... Show more content
on Helpwriting.net ...
The marketing management thinks that market shipping new service nationally successful that the expected profits (excluding the cost of the market
study) will be ВҐ1,600,000 however if the market shipping new service nationally failure then it expected loss of ВҐ700,000(excluding the cost of the
market study). However absence of market study, there are equal chances of national success and national failure after if China Shipping (Group)
Company decide to market nationally. Therefore now the marketing management has to determine the best strategy that China Shipping (Group)
Company should adopt.
Excel
According to the decision tree above, the optimal decision for China Shipping (Group) Company is to carry out test market and then market nationally
if national success then the company will have return in expected profit of ВҐ654,000 compared to do not conduct test market only have expected
profit of ВҐ450,000.
Sensitivity analysis
Assuming the probability of national success after the market study will decrease by 15% and the probability of national success without market
study will increase by 10%. If a local success is observed, the new probability will decrease from 80% to 65% that new shipping service will be
national success. If a local failure is observed, the new probability will decrease from 30% to 15% that new shipping service will be will be national
success. However absence of market study and immediately market

Quantitative Techniques
DESCRIPTIVE STATISTICS & PROBABILITY THEORY
1. Consider the following data: 1, 7, 3, 3, 6, 4 the mean and median for this data are a. 4 and 3 b. 4.8 and 3 c. 4.8 and 3 1/2 d. 4 and 3 1/2 e. 4 and 3 1/3
2. A distribution of 6 scores has a median of 21. If the highest score increases 3 points, the median will become __. a. 21 b. 21.5 c. 24 d. Cannot be
determined without additional information. e. none of these
3. If you are told a population has a mean of 25 and a variance of 0, what must you conclude? a. Someone has made a mistake. b. There is only one
element in the population. c. There are ... Show more content on Helpwriting.net ...
All of the other passengers are sober, and will go to their proper seats unless it is already occupied; In that case, they will randomly choose a free
seat. You 're person number 100. What is the probability that you end up in your seat (i.e., seat #100)?. Solution: Let's consider seats #1 and #100.
There are two possible outcomes: E1: Seat #1 is taken before #100; E2: Seat #100 is taken before #1. If any passenger takes seat #100 before #1 is
taken, surely you will not end up in you own seat. But if any passenger takes #1 before #100 is taken, you will definitely end up in you own seat.
By symmetry, either outcome has a probability of 0.5. So the probability that you end up in your seat is 50%. Explanation: If the drunk passenger
takes #1 by chance, then it's clear all the rest of the passengers will have the correct seats. If he takes #100, then you will not get your seat. The
probabilities that he takes #1 or #100 are equal. Otherwise assume that he takes the n–th seat, where n is a number between 2 and 99. Everyone
between 2 and (n–1) will get his own seat. That means the n–th passenger essentially becomes the new "drunk" guy with designated seat #1. If he
chooses #1, all the rest of the passengers will have the correct seats. If he takes #100, then you will not get your seat. (The probabilities that he takes
#1 or #100 are again

Project Completion Method: Stochastic Project Scheduling...
Manuscript ID: CO/2003/022870 Specialty Area: Cost & Schedule Audience: Researchers PROBABILITY OF PROJECT COMPLETION USING
STOCHASTIC PROJECT SCHEDULING SIMULATION (SPSS) Dong–Eun Lee1 ABSTRACT This paper introduces a software, Stochastic Project
Scheduling Simulation (SPSS), developed to measure the probability to complete a project in a certain time specified by the user. To deliver a project
by a completion date committed to in a contract, a number of activities need to be carried out. The time that an entire project takes to complete and the
activities that determine total project duration are always questionable because of the randomness and stochastic nature of the activities' durations.
Predicting a project completion probability... Show more content on Helpwriting.net ...
It means PERT assumes that the duration of each activity is represented by arandom variable with a known probability density function. PERT extends
CPM by introducing the concept of uncertainty in estimating activity durations. "PERT uses expected mean time (te) with standard deviation or
variance. The expected mean time (te) of an individual activity is an estimate having an approximate chance of 50 percent success. Three time
estimates, i.e., the most likely (m), optimistic (a), and pessimistic (b) durations, are required for each activity." (Khisty and Mohammadi; 2001). But
PERT has also been criticized for systematically underestimating the total project duration. That is why a new methodology is required to increase the
accuracy of scheduling project activities. As stated by Crandall (1977), the most reliable method of predicting the total behavior or a network
comprised of probabilistic activities is simulation. To complement the PERT system, simulation can be applied to run a network a certain number of
times. Complementing the existing approaches with simulation can reduce the errors that might be introduced by the PERT assumptions as studied by
MacCrimmon and Ryavec (1962) and Van Slyke (1963). The Probability Density Function (PDF) of the duration of a construction activity is unknown
and needs to be selected depending on the type of project. In general, the variability of the time estimates of an activity can be assumed to follow the
Beta distribution.

Graph Investigation
–What features of the graph would you need for the expected proportionality to be verified? In other words, what should the graph look like to verify
the inverse square law?(2 marks) The inverse square law states, that the intensity of the luminosity is inversely proportional to the square of the
distance from the source. The graph would require features such as; evidence that the increase in distance away from the source results in the
reduction of light exposure as well as, the contrast between the ascending distance and descending LUX, in which forms an 'X' within the graph in
order to verify the proportionality expected. This can be seen on the graph, when the distance d from the source is doubled, the same amount of light is
distributed... Show more content on Helpwriting.net ...
The classroom, although the blinds were drawn, allowed a large amount of light in; from the cracks in the blinds and the glare from the uncovered
windows connecting to the hallway. This may have affected our results as the beam of light being projected out of the light box may have lost its
intensity; also resulting in the light metre picking up the surrounding light as well as the dull light beam. Ultimately, we may have collected inaccurate
data due to the excess of light. The instrument used to measure the apparent magnitude of the star (light box beam) in our practical, had no way of
displaying if it was perpendicular to the desk. We noticed whilst using the light metre, a slight tilt of the instrument could increase or decrease the
amount of light being detected, changing the figure displayed on the screen. As the person responsible for holing the instrument, I found it rather
challenging to keep it at the same angle for every increment. The change of angle and light detected could have interfered with our data

Essay about Dai Park Textbook
Stochastic Manufacturing & Service Systems Jim Dai and Hyunwoo Park School of Industrial and Systems Engineering Georgia Institute of
Technology October 19, 2011 2 Contents 1 Newsvendor Problem 1.1 Proп¬Ѓt Maximization 1.2 Cost Minimization . 1.3 Initial Inventory . . 1.4
Simulation . . . . . . 1.5 Exercise . . . . . . . 5 5 12 15 17 19 25 25 27 29 29 31 32 33 34 39 39 40 40 42 44 46 47 48 49 51 51 51 52 54 55 57 . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... Show
more content on Helpwriting.net ...
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Exercise Answers 6.1 Newsvendor Problem . . . . . . . 6.2 Queueing
Theory . . . . . . . . . 6.3 Discrete Time Markov Chain . . 6.4 Poisson Process . . . . . . . . . . 6.5 Continuous Time Markov Process . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 1 Newsvendor Problem In this course, we will
learn how to design, analyze, and manage a manufacturing or service system with uncertainty. Our п¬Ѓrst step

Monte Carlo Simulation : A Computerized Mathematical...
I. Introduction The Monte Carlo Simulation is a computerized mathematical technique that allows people to account for risk in quantitative analysis
and decision. It furnishes the decision–maker with a range of possible outcomes and probabilities that they will occur for any chance of action. It
shows the extreme possibilities of things as well. The system calculates results over and over, each time using a different set of random values
from the probability functions. The simulation could involve tens and thousands of recalculations before its complete. There will be many
different probability distributions. In this exploration I will find how to use the Monte Carlo Simulation in order to find future stock prices for
the Gold Share Market (GLD). II. Exploration First, we need to go in depth and see what we need to find in order to start the simulation. Each
day, the the price of an asset, such as a stock is: Today's Stock Price= Yesterday's Stock Price x er r=periodic daily return, the rate that the asset
increased or decreased that day. Because the rate of return on an asset is a random number, to model the movement to determine possible future
values, a formula is needed that model random movements. This was first done about 100 years ago by Louis Bachelier who first applied the
Brownian Motion; a formula used to model random movements and physics to the movement of the price of an asset. His work expanded on the Black
Scholes Finance formula, and some of

Tutorial on Probablity
Mathematics Department
Tutorial Sheet No. 3
MAL250(Probability and Stochastic Processes)
1. The percentage of alcohol (100X ) in a certain compound may be considered as a random variable, where
X (0 < X < 1) has pdf fX (x) = 20x3 (1 в€’ x), 0 < x < 1.
Suppose that the selling price of the above compound depends on the alcohol contents. Speciп¬Ѓcally, if
1/3 < X < 2/3, the compound sells for c1 dollars/gallon otherwise it sells for c2 dollars/gallon. If the cost is c3 dollars/gallon, п¬Ѓnd the probability
distribution of the net proп¬Ѓt per gallon.
2. The pdf of a random variable X is given by fX (x) = 6x(1 в€’ x), 0 < x < 1.
Find the distribution of
(i) Y = X/X+1
пЈ±
пЈІ 2X, в€’в€
ћ < X < 1/4
1
, 1/4 в‰¤ X < 3/4
(ii) Y =
2
пЈі2
, 3/4 в‰¤ X < в€
ћ. ... Show more content on Helpwriting.net ...
Also п¬Ѓnd the variance of the proп¬Ѓt P.
17. Suppose that an electronic device has a life length X (in units of 100 hours) which is considered as a continuous random variable with the pdf fX
(x) = eв€’x , x > 0. Suppose that the cost of manufacturing such item is $2.00. The manufacturer sells the item for $5.00, but guarantees a total refund
if X < 0.9. What is the manufacturer's expected proп¬Ѓt per item?. 18. Suppose that X is a continuous r.v. having the following pdf: f (x)
=
=

ex if x в‰¤ 0
2
eв€’x if x > 0.
2
Let Y = |X |. Obtain E(Y ) and Var(Y ).
19. A company rents out time on a computer for periods of t hours,for which it receives $400 an hour. The number of times the computer breaks down
during t hours is a r.v. having the Poisson distribution with О» = (0.8)t, and if the computer breaks down x times it costs 50x dollars to п¬Ѓx it. How
should the company select t in order to maximize its expected proп¬Ѓt?

Forward Software Settlement or Else
Risk Management: Case Analysis Submission (Forward Software) 1. Introduction and problem statement
Focus software with its Focus A–B–C is the current market leader in the spreadsheet market. Focus Software, being the first mover with its intuitive
menu system with functionality like macros had the largest market share with only one flaw, of printing graphs. Discount Software, with its VIP
Scheduler had the same menu system to ease the user in making the transition to its software whereas Cinco, a Forward Software product, gave the
users the options of either using its own menu system or a Focus style menu system with all the functionalities like and inbuilt graph printing ability.
With the current legal proceedings initiated by Focus ... Show more content on Helpwriting.net ...
loss if he conducts survey ($4.64 million, includes research cost) > loss if he doesn't conduct the survey ($4.5 million). * The research cost for the
survey should not greater than $ 0.564 million * If he doesn't conduct the survey he should wait for Focus –Discount trial result as the loss is less, if he
doesn't wait and tries to settle it outside. In case the Focus wins the case and files another against Forward, it would be optimum for Forward to settle
it outside court
3. Basic Tree Diagram
Please refer to the attached Excel Sheet for the Tree Diagram 4. Analysis related to hiring the outside law firm and sensitivity of the value of
information to their prediction accuracy
We have tried to find the expected final monetary value (final output, in the graph Figure 1) by varying the cost of survey charged by the law firm
keeping the accuracy constant at 0.9. Without considering the impact of fees charged by the law research firm, the cost of survey should not be greater
than $ 0.9 million
In figure 2, we have varied the prediction accuracy of the law research firm and based on the graph we have come to the conclusion that with
associated cost of $ 0.7 million the research firm should have accuracy greater than 0.9 to reduce the expected monetary value than $ 4.5 million 5.
Probability distribution of costs under optimal decisions and sensitivity analysis of optimal cost with various parameters
In figure 3, we have calculated EMV for

Advantages And Disadvantages Of Density Forecasts
The density forecast of a random variable is an estimation based on the past observed data. This is a symmetric interval prediction which means that
the outcomes will fall into an interval that is a band of plus/minus a fixed times of standard errors. The estimation provides a probability distribution of
all possible future values of that variable. Over the past decades, the price density forecast has been widely used to study microeconomic and financial
issues. Forecasting the future development of the economy is of great importance for proper government monetary decisions and individual risk
management. A good macroeconomic density forecast presents a subjective description of inflationary pressure and other information related to
economics.... Show more content on Helpwriting.net ...
Although the methods they first used have many drawbacks, these analyses still help governments in understanding the macroeconomic environment
and making adjustments to current monetary policy. The oldest quarterly survey of macroeconomics forecasts in the US is the Survey of Professional
Forecasters (SPF) whose name changed to ASA–NBER survey later (Diebold, Tay and Wallis,

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