Probability and Statistics

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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

Chapters: 22(22.2 , 22.3, 22.5,22.6,22.7(Except Hypergeometric Distribution) , 22.8); 23(23.1,23.2,23.3, 23.9,22.10)

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

Sample spaces and events

Session 2

Axiomatic definition of probability

Session 3

Axioms and Properties of Probability

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

Session 7

Dependent and Independence Events

Session 8

Conditional Probability

Session 9 & 10

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

Session 11

Discrete random variables and probability distributions

Session 12

Continuous random variables and probability distributions

Session 13

Mean ,Variance and Moment Generating Function of Distributions

Session 14 & 15

Project -3
Application of random variables in  Engineering Field

Session 16

Uniform Distribution

Session 17

Binomial Distribution

Session 18

Poisson Distribution

Session 19 & 20

Project-4
Applications of  Poisson distribution

Session 21

Normal Distribution

Session 22

Working with Normal Tables

Session 23

Normal Approximation to the Binomial Distributions

Session 24 & 25

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

Session 26

Random Sampling, Population and Sample

Session 27

Sample Mean and Variances, Point and Interval Estimations

Session 28

Confidence Intervals

Session 29

Correlation Coefficient

Session 30

Co-variance independent random variables

Session 31

Linear Regression of two variables

Session 32 & 33

Project -6
Uses of Regression and Correlation Analysis in Business

Case Studies

Dr.Banitamani Mallik

TEACHER
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Professor ,School of Applied Sciences, Centurion University of Technology and Management, Paralakhemundi, Odisha, India. She has over 26 years of teaching and 8 years of research experiences. She has published 35 research articles in National and International refereed journals and has authored 01 book and 02 book chapters. She has produced 01 PhD scholar and […]