1) The document provides examples of curve sketching functions by finding the derivatives, critical points, relative extrema, inflection points, and concavity.
2) In one example, a function is graphed and is found to have a relative maximum at (-3,14) and a relative minimum at (1,-18).
3) Another example finds the relative extrema of a cubic function, which has a relative maximum at (-1,4) and a relative minimum at (1,0), as well as an inflection point at (0,2).
It includes concepts of logarithms including properties and log tables. The methodology to find out values using log tables and anti log tables is also mentioned in a detailed manner. Moreover, questions related to logarithms are mentioned for practice.
It includes concepts of logarithms including properties and log tables. The methodology to find out values using log tables and anti log tables is also mentioned in a detailed manner. Moreover, questions related to logarithms are mentioned for practice.
Statistics Assignment 1 HET551 – Design and Developm.docxrafaelaj1
Statistics Assignment 1
HET551 – Design and Development Project 1
Michael Allwright
Haddon O’Neill
Tuesday, 24 May 2011
1 Normal Approximation to the Binomial Distribution
This section of the assignment shows how a normal curve can be used to approximate the binomial distribution. This
section of the assignment was completed using a MATLAB function (shown in Listings 1) which would generate and
save plots of the various Binomial Distributions after normalisation, and then calculate the errors between the standard
normal curve and the binomial distribution.
The plots in Figures 1 and 2 show the binomial distribution for various n trials with probability p = 1
3
and p = 1
2
respectively. These binomial plots have been normalised so that they can be compared with the standard normal
distribution.
From these plots it can be seen that once the binomial distribution has been normalised, the normal approximation is
a good approach to estimating the binomial distribution. To determine its accuracy, the data in Table 1 shows the
evaluation of qn = P(bn ≥ µn + 2σn) for both the normal curve and binomial distribution.
qn = P(bn ≥ µn + 2σn) Calculation Error
n N(0, 1) B(n, 1
2
) B(n, 1
3
) B(n, 1
2
) B(n, 1
3
)
1 0.0228 0.0000 0.0000 -0.02278 -0.02278
2 0.0228 0.0000 0.0000 -0.02278 -0.02278
3 0.0228 0.0000 0.0370 -0.02278 0.01426
4 0.0228 0.0000 0.0123 -0.02278 -0.01043
5 0.0228 0.0313 0.0453 0.00847 0.02249
10 0.0228 0.0107 0.0197 -0.01203 -0.00312
20 0.0228 0.0207 0.0376 -0.00208 0.01486
30 0.0228 0.0214 0.0188 -0.00139 -0.00398
40 0.0228 0.0192 0.0214 -0.00354 -0.00134
50 0.0228 0.0164 0.0222 -0.00636 -0.00059
100 0.0228 0.0176 0.0276 -0.00518 0.00479
Table 1: Calculating the error of the normal approximation to the binomial for various n and p
2 Analytical investigation of the Exponential Distribution
For this part of the assignment the density function shown in Equation 1 was given.
f(x) = λe−λx for x ≥ 0 and λ ≥ 0 (1)
Before any calculations were attempted, the area under graph was checked to show that
´∞
−∞f(x) dx = 1. That is
that the total probability of all possible values was 1.
2.1 Derivation of CDF
To find the CDF of the given function, the function was integrated with 0 and x being the lower and upper bound
respectively. This derivation is shown in Equations 2 to 4.
CDF =
ˆ x
o
f(x) dx =
ˆ x
o
λe−λx dx (2)
2
−5 −4 −3 −2 −1 0 1 2 3 4 5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Number of Successes (shifted left by u = 0.33)
P
ro
b
a
b
ili
ty
(a) n = 1
−5 −4 −3 −2 −1 0 1 2 3 4 5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Number of Successes (shifted left by u = 0.67)
P
ro
b
a
b
ili
ty
(b) n = 2
−5 −4 −3 −2 −1 0 1 2 3 4 5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Number of Successes (shifted left by u = 1.00)
P
ro
b
a
b
ili
ty
(c) n = 3
−5 −4 −3 −2 −1 0 1 2 3 4 5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Number of Successes.
This learner's module discusses or talks about the topic of Quadratic Functions. It also discusses what is Quadratic Functions. It also shows how to transform or rewrite the equation f(x)=ax2 + bx + c to f(x)= a(x-h)2 + k. It will also show the different characteristics of Quadratic Functions.
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.
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
#vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore#blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #blackmagicforlove #blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #Amilbabainuk #amilbabainspain #amilbabaindubai #Amilbabainnorway #amilbabainkrachi #amilbabainlahore #amilbabaingujranwalan #amilbabainislamabad
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.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.