: Random Variable, Discrete Random variable, Continuous random variable, Probability Distribution of Discrete Random variable, Mathematical Expectations and variance of a discrete random variable.
: Random Variable, Discrete Random variable, Continuous random variable, Probability Distribution of Discrete Random variable, Mathematical Expectations and variance of a discrete random variable.
Chapter 4 part3- Means and Variances of Random Variablesnszakir
Statistics, study of probability, The Mean of a Random Variable, The Variance of a Random Variable, Rules for Means and Variances, The Law of Large Numbers,
3rd and 4th Class, Claregalway NS show some decoration tipps for winter.
This presentation is part of the Comenius-project "WATER IN OUR LIVES"
"This project has been funded with support from the European Commission. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein."
Probability
Random variables and Probability Distributions
The Normal Probability Distributions and Related Distributions
Sampling Distributions for Samples from a Normal Population
Classical Statistical Inferences
Properties of Estimators
Testing of Hypotheses
Relationship between Confidence Interval Procedures and Tests of Hypotheses.
Detail Description about Probability Distribution for Dummies. The contents are about random variables, its types(Discrete and Continuous) , it's distribution (Discrete probability distribution and probability density function), Expected value, Binomial, Poisson and Normal Distribution usage and solved example for each topic.
Chapter-4: More on Direct Proof and Proof by Contrapositivenszakir
Proofs Involving Divisibility of Integers, Proofs Involving Congruence of Integers, Proofs Involving Real Numbers, Proofs Involving sets, Fundamental Properties of Set Operations, Proofs Involving Cartesian Products of Sets
Chapter 6 part2-Introduction to Inference-Tests of Significance, Stating Hyp...nszakir
Mathematics, Statistics, Introduction to Inference, Tests of Significance, The Reasoning of Tests of Significance, Stating Hypotheses, Test Statistics, P-values, Statistical Significance, Test for a Population Mean, Two-Sided Significance Tests and Confidence Intervals
Chapter 6 part1- Introduction to Inference-Estimating with Confidence (Introd...nszakir
Introduction to Inference, Estimating with Confidence, Inference, Statistical Confidence, Confidence Intervals, Confidence Interval for a Population Mean, Choosing the Sample Size
Chapter 5 part2- Sampling Distributions for Counts and Proportions (Binomial ...nszakir
Mathematics, Statistics, Sampling Distributions for Counts and Proportions, Binomial Distributions for Sample Counts,
Binomial Distributions in Statistical Sampling, Binomial Mean and Standard Deviation, Sample Proportions, Normal Approximation for Counts and Proportions, Binomial Formula
Chapter 5 part1- The Sampling Distribution of a Sample Meannszakir
Mathematics, Statistics, Population Distribution vs. Sampling Distribution, The Mean and Standard Deviation of the Sample Mean, Sampling Distribution of a Sample Mean, Central Limit Theorem
Mathematics, Statistics, Probability, Randomness, General Probability Rules, General Addition Rules, Conditional Probability, General Multiplication Rules, Bayes’s Rule, Independence
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
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Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
Vaccine management system project report documentation..pdf
Chapter 4 part2- Random Variables
1. INTRODUCTION TO
STATISTICS & PROBABILITY
Chapter 4:
Probability: The Study of Randomness
(Part 2)
Dr. Nahid Sultana
1
2. Chapter 4
Probability: The Study of Randomness
4.1 Randomness
4.2 Probability Models
4.3 Random Variables
4.4 Means and Variances of Random Variables
4.5 General Probability Rules*
2
3. 4.3 Random Variables
3
Random Variable
Discrete Random Variables
Continuous Random Variables
Normal Distributions as Probability Distributions
4. 4
Random Variables
4
A probability model: sample space S and probability for each outcome.
A numerical variable that describes the outcomes of a chance process is
called a random variable.
The probability model for a random variable is its probability distribution.
The probability distribution of a random variable gives its possible
values and their probabilities.
Example: Consider tossing a fair coin 3 times.
Define X = the number of heads obtained.
X = 0: TTT
X = 1: HTT THT TTH
X = 2: HHT HTH THH
X = 3: HHH
Value 0 1 2 3
Probability 1/8 3/8 3/8 1/8
5. 5
Discrete Random Variable
Two main types of random variables: discrete and continuous.
A discrete random variable X takes a fixed set of possible values
with gaps between.
The probability distribution of a discrete random variable X lists the
values xi and their probabilities pi:
The probabilities pi must satisfy two requirements:
1. Every probability pi is a number between 0 and 1.
2. The sum of the probabilities is 1.
6. 6
Discrete Random Variable (Cont…)
Example: Consider tossing a fair coin 3 times.
Define X = the number of heads obtained.
X = 0: TTT
X = 1: HTT THT TTH
X = 2: HHT HTH THH
X = 3: HHHValue 0 1 2 3
Probability 1/8 3/8 3/8 1/8
Q1: What is the probability of tossing at least two heads?
Ans: P(X ≥ 2 ) = P(X=2) + P(X=3) = 3/8 + 1/8 = 1/2
Q2: What is the probability of tossing fewer than three heads?
Ans: P(X < 3 ) = P(X=0) +P(X=1) + P(X=2) = 1/8 + 3/8 + 3/8
= 7/8
Or P(X < 3 ) = 1 – P(X = 3) = 1 – 1/8 = 7/8
7. 7
Discrete Random Variable (Cont…)
Example: North Carolina State University posts the grade distributions for its
courses online. Students in one section of English210 in the spring 2006
semester received 31% A’s, 40% B’s, 20% C’s, 4% D’s, and 5% F’s.
The student’s grade on a four-point scale (with A = 4) is a random
variable X. The value of X changes when we repeatedly choose students at
random , but it is always one of 0, 1, 2, 3, or 4. Here is the distribution of X:
Q1: What is the probability that the
student got a B or better?
Ans: P(X ≥ 3 ) = P(X=3) + P(X=4)
= 0.40 + 0.31 = 0.71
Q2: Suppose that a grade of D or F in English210 will not count as satisfying
a requirement for a major in linguistics. What is the probability that a
randomly selected student will not satisfy this requirement?
Ans: P(X ≤ 1 ) = 1 - P( X >1) = 1 – ( P(X=2) + P(X=3) + P(X=4) ) = 1- 0.91 = 0.09
8. 8
Continuous Random Variable
A continuous random variable Y takes on all values in an interval of
numbers.
Ex: Suppose we want to choose a number at random between 0 and 1.
-----There is infinitely many number between 0 and 1.
How do we assign probabilities to events in an infinite sample space?
The probability distribution of Y is described by a density curve.
The probability of any event is the area under the density curve and
above the values of Y that make up the event.
9. 9
A discrete random variable X has a finite number of possible values.
The probability model of a discrete random variable X assigns a
probability between 0 and 1 to each possible value of X.
A continuous random variable Y has infinitely many possible values.
The probability of a single event (ex: X=k) is meaningless for a
continuous random variable. Only intervals can have a non-zero
probability; represented by the area under the density curve for that
interval .
Discrete random variables commonly arise from situations that
involve counting something.
Situations that involve measuring something often result in a
continuous random variable.
Continuous Random Variable (Cont…)
10. 10
Continuous Probability Models
Example: This is a uniform density curve for the variable X. Find the
probability that X falls between 0.3 and 0.7.
Ans: P(0.3 ≤ X ≤ 0.7) = (0.7- 0.3) * 1 = 0.4
Uniform
Distribution
11. 11
Continuous Probability Models (Cont…)
Example: Find the probability of getting a random number that is
less than or equal to 0.5 OR greater than 0.8.
P(X ≤ 0.5 or X > 0.8)
= P(X ≤ 0.5) + P(X > 0.8)
= 0.5 + 0.2
= 0.7
Uniform
Distribution
12. 12
Continuous Probability Models (Cont…)
General Form:
The probability of the event A is the shaded area under the density
curve. The total area under any density curve is 1.
13. 13
Normal Probability Model
The probability distribution of many random variables is a normal
distribution.
Example: Probability distribution
of Women’s height.
Here, since we chose a woman
randomly, her height, X, is a
random variable.
To calculate probabilities with the normal distribution, we standardize
the random variable (z score) and use the Table A.
14. 14
Normal Probability Model (Cont…)
Reminder: standardizing N(µ,σ)
We standardize normal data by calculating z-score so that any normal
curve can be transformed into the standard Normal curve N(0,1).
σ
µ)( −
=
x
z
15. 15
Normal Probability
Model (Cont…)
Women’s heights are normally
distributed with µ = 64.5 and σ = 2.5
in.
The z-scores for 68,
And for x = 70",
4.1
5.2
)5.6468(
=
−
=z
z =
(70−64.5)
2.5
= 2.2
The area under the curve for the interval
[68”,70”] is 0.9861-0.9192=0.0669.
Thus the probability that a randomly
chosen woman falls into this range is
6.69%. i.e.
P(68 ≤ X ≤ 70)= 6.69%.
What is the probability, if we pick one woman at random, that her height
will be between 68 and 70 inches i.e. P(68 ≤ X ≤ 70)? Here because the
woman is selected at random, X is a random variable.