# Probability and Statistics

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Course Name :Probability and Statistics

Code(Credit) : CUTM1524(3-1-2)

## Course Objectives

• To translate real-world problems into probability models.
• To motivate students in an intrinsic interest in statistical thinking.
• T o apply probability and statistics in engineering and science like disease modeling, climate prediction and computer networks etc.

## Learning Outcomes

Upon successful completion of this course, students will be able to:

•Define and illustrate the concepts of sample space, events and compute the probability and conditional probability of events.
•Define, illustrate and apply the concepts of discrete and continuous random variables, the discrete and continuous probability distributions.
•Define, illustrate and apply the concept of the expectation to the mean, variance and covariance of random variables.
•Compute probabilities based on practical situations using the Binomial, Poisson and Normal distributions.

## Course Syllabus

Module I: (4 hrs+2 hrs+4hrs)

Probability: Axiomatic definitions of probability, Sample Space, Probability axioms, Independent events, Mutually Exclusive Event, Equally Likely Events

Practice-1(2 hrs)

Bayes Theorem using MATLAB

Project-1 (2hrs)

Application of conditional probability analysis to the clinical diagnosis

Project-2(2hrs)

A Report on Bayes’ Theorem and its Application in Different Fields

Module II:(4 hrs+2 hrs+4hrs)

Discrete random variables, Continuous random variables, Expectation of random variables,Variance and Standard Deviation

Practice-2(2hrs)

Probability Density Function using MATLAB

Project-3(2hrs)

A Report on Random Variables with Examples

Project-4 (2hrs)

A Report on Moment Generating Function of Distributions

Module III:(6 hrs+4 hrs+4hrs)

Binomial distribution, Poisson distribution, Poisson Distribution as the limiting case of Binomial Distribution

Practice-3(2 hrs)

Binomial distribution using MATLAB

Practice-4(2 hrs)

Poisson distribution - algorithm in Matlab

Project-5(2hrs)

Comparative study between Binomial distribution and Poisson distribution

Project-6(2hrs)

Report on Poisson distribution with their Business Applications in analyzing
data sets

Module IV:(4 hrs+2hrs+8hrs)

Uniform distribution, Normal distributions, Normal approximation to the Binomial distributions

Practice-5(2hrs)

Gaussian distribution – how to plot it in Matlab

Project -7(2hrs)

Flip class

A Report on Gamma, Exponential, Beta Distributions

Project-8(2hrs)

A Report on Central Limit Theorem (CLT) and its Applications in election polls

Project-9(2hrs)

Flip class

A Report on Negative binomial Distribution

Project-10(2hrs)

Flip class

A Report on Geometric distributions

Module V:(4 hrs+0 hr+0 hr)

Distribution of two random variables, Expectation of function of two random variables

Module VI:(4 hrs)

Conditional distributions and expectations.

Module VII:(4 hrs+2 hrs+4hrs)
Correlation coefficient, Co-variance independent random variables, linear regression of two variables

Practice-6(2hrs)

Covariance & Correlation Coefficient calculation in MATLAB

Project-11 (2hrs)

Flip Class

A Report on Markov’s inequality

Project -12(2hrs)

Flip Class

A Report on Chebyshev’s inequality
Total Hrs=T(30hrs+P(12hrs)+Pj(24hrs))

Text Books:
1. Irwin Miller and Marylees Miller, John E. Freund, Mathematical Statistics with Applications, 7th Ed., Pearson Education, Asia, 2006.
2. Sheldon Ross, Introduction to Probability Models, 9th Ed., Academic Press, Indian Reprint, 2007.
Reference Books:
1. Statistical Methods By S.P. Gupta (31st Edition) ; Publisher: Sultan Chand & Sons
2. Mathematical Statistics By S.C. Gupta & V.K. Kapur(10th Edition); Publisher: Sultan Chand & Sons.
Course outline Prepared by: Dr.Banitamani Mallik

Date:08-06-2020

Source of reference: udemy,coursera, Harvard University

Note: 1 credit theory=10 hrs lecture, 1 credit practice/project=12.5 hrs lab/workshop/field work in a semester

## Session 1

Axiomatic definitions of probability, Sample Space

PPT-1(Basics of Probability)

## Session 2

Probability axioms, Independent events

PPT2- PROBABILITY IN REAL LIFE

## Session 3

Mutually Exclusive Event, Equally Likely Events

PPT3(Examples of Probability)

## Session 4

Independent and Dependent Events

PPT4(INDEPENDENT AND DEPENDENT EVENTS)

Bayes Theorem

## Session 6

Practice-1
Bayes Theorem using MATLAB

## Session 7

Project-1

Conditional probability

PPT5(Conditional Probability)

## Session  8

Project-1

Application of conditional probability analysis to the clinical diagnosis

PPT6-(Application of conditional probability)

## Session 9

Project-2
A Report on Bayes’ Theorem and its Application in Different Fields

## Session 10

A Report on Bayes’ Theorem and its Application in Different Fields

## Session 11

Discrete random variables

PPT7(Random Variables)

## Session 12

Continuous random variables

PPT8(Application of Random Variables)

## Session 13

Expectation of random variables

## Session 14

Variance and Standard Deviation

## Session 15

Practice-2
Probability Density Function using MATLAB

## Session 16

Practice-2
Probability Density Function using MATLAB

## Session 17

Project-3
A Report on Random Variables with Examples

## Session 18

Project-3
A Report on Random Variables with Examples

PPT9(RV)

## Session 19

Moment Generating Function of Distributions

## Session 20

Project-4
A Report on Moment Generating Function of Distributions

## Session 21

Binomial distribution

## Session 22

Binomial distribution

PPT10(Binomial Distribution).

## Session 23

Binomial distribution

PPT11(Binomial Distribution)

## Session 24

Poisson distribution

## Session 25

Poisson distribution

PPT12(Poisson Distribution)

## Session 26

Poisson Distribution as the limiting case of Binomial
Distribution

## Session 27

Practice-3
Binomial distribution using MATLAB
http://www.matrixlab-examples.com/binomial-distribution.html

## Session 28

Practice-3
Binomial distribution using MATLAB

## Session 29

Practice-4
Poisson distribution - algorithm in Matlab
http://www.matrixlab-examples.com/poisson-distribution.html

## Session 30

Practice-4
Poisson distribution - algorithm in Matlab

## Session 31

Project-5

Comparative study between Binomial distribution and Poisson distribution

## Session 32

Project-5

Comparative study between Binomial distribution and Poisson distribution

## Session 33

Project-6
Report on Binomial and Poisson distribution with their Business Applications in analyzing data sets

## Session  34

Project-6
Report on Binomial and Poisson distribution with their Business Applications in analyzing data sets

## Session 35

Uniform distribution

PPT13(Uniform Distribution )

## Session 36

Normal distributions

## Session 37

Normal distributions

PPT14-Normal Distribution

## Session 38

Normal approximation to the Binomial distributions

## Session 39

Practice-5
Gaussian distribution – how to plot it in Matlab
http://www.matrixlab-examples.com/gaussian-distribution.html

## Session  40

Gaussian distribution

PPT15(Normal Distribution)

## Session 41

Project-7

Flip class

A Report on Gamma Distributions

## Session  42

Project-7

A Report on Exponential, Beta Distributions

## Session 43

Project-8

A Report on Central Limit Theorem (CLT) and its Applications in election polls

## Session 44

A Report on Central Limit Theorem (CLT) and its Applications in election polls

## Session 45

Project-9

Flip class

A Report on Negative binomial Distribution

## Session  46

Project-9

Flip class

A Report on Negative binomial Distribution

## Session 47

Project-10

Flip class

A Report on Geometric distributions

## Session 48

Project-10

Flip class

A Report on Geometric distributions

## Session 49

Joint Probability Distribution of two random variables

## Session 50

Joint Probability Distribution of two random variables

## Session 51

Expectation of function of two random variables

## Session 52

Expectation of function of two random variables

## Session 53

Conditional distributions and expectations

## Session 54

Conditional distributions and expectations

## Session 55

Conditional distributions and expectations

## Session 56

Conditional distributions and expectations

## Session 57

Correlation coefficient

PPT16(Uses of regression and correlation analysis in bussines )

## Session 58

Co-variance independent random variables

## Session 59

Linear Regression of two variables

## Session 60

Linear Regression of two variables

PPT17(Regression Analysis)

## Session 61

Practice-6
Covariance & Correlation Coefficient calculation in MATLAB

## Session 62

Practice-6
Covariance & Correlation Coefficient calculation in MATLAB

## Session 63

Project-11

Flip Class
A Report on Markov’s inequality

## Session 64

Project-11

Flip Class
A Report on Markov’s inequality

## Session 65

Project-12

Flip Class
A Report on Chebyshev’s inequality

## Session 66

Project-12

Flip Class
A Report on Chebyshev’s inequality