Probability and Statistics

Teacher

Dr.Banitamani Mallik

Category

Core Courses

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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 Plan

Session 1

Axiomatic definitions of probability, Sample Space
Web Link
https://www.youtube.com/watch?v=ZA4JkHKZM50

PPT-1(Basics of Probability)

Session 2

Probability axioms, Independent events
Web Link
https://www.youtube.com/watch?v=LS-_ihDKr2M

PPT2- PROBABILITY IN REAL LIFE

Session 3

Mutually Exclusive Event, Equally Likely Events

Web Link
https://www.youtube.com/watch?v=7ZK6HuF61pY

PPT3(Examples of Probability)

Session 4

Independent and Dependent Events

Web Link

https://www.youtube.com/watch?v=LS-_ihDKr2M.

PPT4(INDEPENDENT AND DEPENDENT EVENTS)

Session 5

Bayes Theorem

Web Link

https://www.youtube.com/watch?v=XQoLVl31ZfQ.

Session 6

Practice-1
Bayes Theorem using MATLAB
https://www.youtube.com/watch?v=dhsK-mRzxFw

Session 7

Project-1

Conditional probability

Web Link

https://www.youtube.com/watch?v=zuQUpShD3ZQ.

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
Web Link
https://www.youtube.com/watch?v=HZGCoVF3YvM

Session 10

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

Web Link

https://www.youtube.com/watch?v=U_85TaXbeIo.

Session 11

Discrete random variables
Web Link
https://www.youtube.com/watch?v=lHCpYeFvTs0

PPT7(Random Variables)

Session 12

Continuous random variables
Web Link
https://www.youtube.com/watch?v=UVQs9zikfe0

PPT8(Application of Random Variables)

Session 13

Expectation of random variables
Web Link
https://www.youtube.com/watch?v=8i9WUZhpxPE

Session 14

Variance and Standard Deviation
Web Link
https://www.youtube.com/watch?v=MRqtXL2WX2M

Session 15

Practice-2
Probability Density Function using MATLAB
Web Link
https://www.youtube.com/watch?v=8N2fZEKqZhg

Session 16

Practice-2
Probability Density Function using MATLAB

Web Link

https://www.youtube.com/watch?v=8N2fZEKqZhg.

Session 17

Project-3 
A Report on Random Variables with Examples

Web Link

https://www.youtube.com/watch?v=ynJFdCrYvdU.

Session 18

Project-3 
A Report on Random Variables with Examples

PPT9(RV)

Session 19

Moment Generating Function of Distributions

Web Link

https://www.youtube.com/watch?v=MENmUBNEDv8.

Session 20

Project-4 
A Report on Moment Generating Function of Distributions

Web Link

https://www.youtube.com/watch?v=l2sx5_e7mIo.

Session 21

Binomial distribution
Web Link
https://www.youtube.com/watch?v=8idr1WZ1A7Q

Session 22

Binomial distribution

PPT10(Binomial Distribution).

Session 23

Binomial distribution

PPT11(Binomial Distribution)

Session 24

Poisson distribution
Web Link
https://www.youtube.com/watch?v=O-YhNpy7z3I

Session 25

Poisson distribution

PPT12(Poisson Distribution)

Session 26

Poisson Distribution as the limiting case of Binomial
Distribution

Web Link

https://www.youtube.com/watch?v=cmWFNOS0v9w.

Session 27

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

Session 28

Practice-3
Binomial distribution using MATLAB
Web Link

https://www.youtube.com/watch?v=Vub3nSjldiU.

Session 29

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

Session 30

Practice-4
Poisson distribution - algorithm in Matlab
Web Link

https://www.youtube.com/watch?v=yqjME6zcr5I.

Session 31

Project-5

Comparative study between Binomial distribution and Poisson distribution

Web Link

https://www.youtube.com/watch?v=eexQyHj6hEA.

Session 32

Project-5

Comparative study between Binomial distribution and Poisson distribution

Web Link

https://www.youtube.com/watch?v=i1DydN7J2z4.

Session 33

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

Web Link

https://www.youtube.com/watch?v=BbLfV0wOeyc.

Session  34

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

Web Link

https://www.youtube.com/watch?v=Fk02TW6reiA.

Session 35

Uniform distribution
Web Link
https://www.youtube.com/watch?v=wnh7Zj2NYNw

PPT13(Uniform Distribution )

Session 36

Normal distributions
Web Link
https://www.youtube.com/watch?v=mtbJbDwqWLE&pbjreload=101

Session 37

Normal distributions

PPT14-Normal Distribution

Session 38

Normal approximation to the Binomial distributions
Web Link
https://www.youtube.com/watch?v=A2sd09qCvcg

Session 39

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

Session  40

Gaussian distribution
Web Link

https://www.youtube.com/watch?v=mtH1fmUVkfE.

PPT15(Normal Distribution)

Session 41

Project-7 

Flip class

A Report on Gamma Distributions

Web Link

https://www.youtube.com/watch?v=gIsoceE4vhg.

Session  42

Project-7 

A Report on Exponential, Beta Distributions

Web Link

https://www.youtube.com/watch?v=onBoUN5qlXg.

Session 43

Project-8

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

Web Link

https://www.youtube.com/watch?v=b5xQmk9veZ4.

Session 44

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

Web Link

https://www.youtube.com/watch?v=N7wW1dlmMaE.

Session 45

Project-9

Flip class

A Report on Negative binomial Distribution

Web Link

https://www.youtube.com/watch?v=UUzRsQ-8vC8.

Session  46

Project-9

Flip class

A Report on Negative binomial Distribution

Web Link

https://www.youtube.com/watch?v=IBBESd4rU1I.

Session 47

Project-10

Flip class

A Report on Geometric distributions

Web Link

https://www.youtube.com/watch?v=zq9Oz82iHf0.

Session 48

Project-10

Flip class

A Report on Geometric distributions

Web Link

https://www.youtube.com/watch?v=LRchV_OrMzw.

Session 49

Joint Probability Distribution of two random variables
Web Link
https://www.youtube.com/watch?v=_lmwI1sGihA

Session 50

Joint Probability Distribution of two random variables
Web Link

https://www.youtube.com/watch?v=759IvlC3yKY.

Session 51

Expectation of function of two random variables
Web Link
https://www.youtube.com/watch?v=6GfR-WHcbLI

Session 52

Expectation of function of two random variables
Web Link

https://www.youtube.com/watch?v=6GfR-WHcbLI.

Session 53

Conditional distributions and expectations
Web Link
https://www.youtube.com/watch?v=XzZYnq10lMU

Session 54

Conditional distributions and expectations
Web Link

https://www.youtube.com/watch?v=strrrdJivco.

Session 55

Conditional distributions and expectations
Web Link
https://www.youtube.com/watch?v=XzZYnq10lMU

Session 56

Conditional distributions and expectations
Web Link

https://www.youtube.com/watch?v=uYbThumrD14.

Session 57

Correlation coefficient
Web Link
https://www.youtube.com/watch?v=lVOzlHx_15s

PPT16(Uses of regression and correlation analysis in bussines )

Session 58

Co-variance independent random variables
Web Link
https://www.youtube.com/watch?v=CY2R4sz_ww8

Session 59

Linear Regression of two variables
Web Link
https://www.youtube.com/watch?v=zPG4NjIkCjc

Session 60

Linear Regression of two variables
Web Link

https://www.youtube.com/watch?v=K_EH2abOp00.

PPT17(Regression Analysis)

Session 61

Practice-6
Covariance & Correlation Coefficient calculation in MATLAB
Web Link
https://www.youtube.com/watch?v=18U1G_35boU

Session 62

Practice-6
Covariance & Correlation Coefficient calculation in MATLAB
Web Link

https://www.youtube.com/watch?v=u1p4Nz6wZHM.

Session 63

Project-11

Flip Class
A Report on Markov’s inequality

Web Link

https://www.youtube.com/watch?v=5xc48m2k4G8.

Session 64

Project-11

Flip Class
A Report on Markov’s inequality

Web Link

https://www.youtube.com/watch?v=cd7ntlIRKuU.

Session 65

Project-12

Flip Class
A Report on Chebyshev’s inequality

Web Link

https://www.youtube.com/watch?v=d5pnfFvggYk.

Session 66

Project-12

Flip Class
A Report on Chebyshev’s inequality

Web Link

https://www.youtube.com/watch?v=CsyoZhiWibs.

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