Probability and Statistics
Probability and Statistics
Teacher
Dr.Banitamani Mallik
Category
Core Courses
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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.
Course Outcomes
Upon successful completion of this course, students will be able to:
| COs | Course Outcomes | Mapping with COs with POs
(High-H, Low-L, Medium-M) |
| CO1 | Define and illustrate the concepts of sample space, events and compute the probability and conditional probability of events. | PO1(3), PO9(2) |
| CO2 | Define, illustrate and apply the concepts of discrete and continuous random variables, the discrete and continuous
probability distributions. |
PO4(3), PO2(2) |
| CO4 | Define, illustrate and apply the concept of the expectation to the mean, variance and covariance of random variables. | PO3(2) |
| CO5 | Compute probabilities based on practical situations using the Binomial, Poisson and Normal distributions. | PO5(2), PO9(2) |
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 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
Our Main Teachers
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 […]