Probability and Statistics

Teacher

Dr.Banitamani Mallik

Category

Core Courses

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Probability and Statistics

Code (Credit): CUTM1005 (2-0-1)

Course Objectives

•To translate real-world problems into probability models

•To motivate students in an intrinsic interest in statistical thinking

•To 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:(3 hrs+2 hrs)
Sample spaces and events; axiomatic definition of probability; Axioms of Probabilities
Project-1

A Report on Application of probability to control the flow of traffic through a highway system, a telephone interchange, or a computer processor

Module II:(3 hrs +2 hrs)
Mutually Exclusive Events, Dependent and Independent Events. Conditional Probability
Project-2
A Report on  Dependent and Independent Events with Examples
Module III:(3 hrs +2 hrs)
Discrete random variables and probability distributions, Continuous random variables and probability
distributions , Mean ,Variance and Moment Generating Function of Distributions
Project-3
Application of random variables in  Engineering Field
Module IV:(3 hrs +2 hrs)
Uniform Distribution, Binomial Distribution, Poisson Distribution
Project-4
Applications of  Poisson distribution
Module V:(3 hrs +2 hrs)
Normal Distribution, Working with Normal Tables, Normal Approximation to the Binomial Distributions
Project-5
Normal Distribution utilized in statistics, business settings, and government entities.
Module VI:(3 hrs)
Statistics: Random Sampling, Population and Sample, Sample Mean and Variances, Point and Interval Estimations, Confidence Intervals
Module VII:(3 hrs +2 hrs)
Regression and Correlation Analysis: Correlation Coefficient, Co-variance independent random
variables, linear regression of two variables
Project-6
Uses of Regression and Correlation Analysis in Business
Text Books:
1. Name of Author, Title, Publication, Edition
Advanced Engineering Mathematics by E. Kreyszig Publisher: John Willey & Sons Inc-8th Edition

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

Sample spaces and events
Web Link
https://www.youtube.com/watch?v=5oI8-iQqPAI

Session 2

Axiomatic definition of probability
Web Link
https://www.youtube.com/watch?v=srXb-gan3JA

Session 3

Axioms and Properties of Probability
Web Link
https://www.youtube.com/watch?v=J5lDl1ejAcQ

Session 4 & 5

Project-1
A Report on Application of probability to control the flow of traffic through a highway system, a telephone interchange, or a computer processor

Session 6

Mutually Exclusive Events
Web Link
https://www.youtube.com/watch?v=SQLAWVkFk4E

Session 7

Dependent and Independence Events
Web Link
https://www.youtube.com/watch?v=LS-_ihDKr2M

Session 8

Conditional Probability
Web Link
https://www.youtube.com/watch?v=bgCMjHzXTXs

Session 9 & 10

Project -2
A Report on  Dependent and Independent Events with Examples

Session 11

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

Session 12

Continuous random variables and probability distributions
Web Link
https://www.youtube.com/watch?v=BW5ndQ33Oqg

Session 13

Mean ,Variance and Moment Generating Function of Distributions
Web Link
https://www.youtube.com/watch?v=b9a27XN_6tg

Session 14 & 15

Project -3
Application of random variables in  Engineering Field

Session 16

Uniform Distribution
Web Link
https://www.youtube.com/watch?v=LoWAy8NtvaI

Session 17

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

Session 18

Poisson Distribution
Web Link
https://www.youtube.com/watch?v=jmqZG6roVqU

Session 19 & 20

Project-4
Applications of  Poisson distribution

Session 21

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

Session 22

Working with Normal Tables

Session 23

Normal Approximation to the Binomial Distributions
Web Link
https://www.youtube.com/watch?v=P3ZpHlzWnMs

Session 24 & 25

Project-5
Normal Distribution utilized in statistics, business settings, and government entities.

Session 26

Random Sampling, Population and Sample
Web Link
https://www.youtube.com/watch?v=yx5KZi5QArQ

Session 27

Sample Mean and Variances, Point and Interval Estimations
Web Link
https://www.youtube.com/watch?v=cmtBUWCC-6A

Session 28

Confidence Intervals
Web Link
https://www.youtube.com/watch?v=MbXThbTSrVI

Session 29

Correlation Coefficient
Web Link
https://www.youtube.com/watch?v=xTpHD5WLuoA

Session 30

Co-variance independent random variables
Web Link
https://www.youtube.com/watch?v=RND_35GMP_c

Session 31

Linear Regression of two variables
Web Link
https://www.youtube.com/watch?v=wRZwrcPnmc4

Session 32 & 33

Project -6
Uses of Regression and Correlation Analysis in Business

Case Studies

Case Studies

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