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SEMESTER II

B5 – DISCIPLINE SPECIFIC MINOR COURSE
KU2DSCSTA131: PROBABILITY AND RANDOM VARIABLES
Semester Course Type Course Level Course Code Credits Total Hours
II MINOR 100 – 199 KU2DSCSTA131 4 60

Learning Approach (Hours/Week) / Marks Distribution
Lecture Practical/Internship Tutorial CE ESE Total Duration of ESE (Hours)
4 - - 30 70 100 2
Course Description

This course delves into probability theory, random variables, bivariate random variables, and correlation and regression analysis, covering topics such as definitions of probability, conditional probability, probability distributions, random variable transformations, joint and marginal probability distributions, correlation analysis, and regression analysis techniques.

Course Prerequisite

HSE level Mathematics/Statistics Courses

Course Outcomes
CO No. Expected Outcome Learning Domains
1 Students will grasp the concepts of random experiments and probability, including frequency, classical, and axiomatic definitions. U
2 Students will comprehend the definitions of discrete and continuous random variables and their probability mass and density functions. R
3 Students will understand the concept of bivariate random variables and they will be able to compute conditional distributions and determine the independence of random variables. A
4 Students will understand the concepts of correlation and its different types, and able to perform simple linear regression, including fitting regression lines and understanding regression coefficients. An
5 Students will be able to apply correlation and regression analysis, probability theory, random variables, and bivariate random variables to analyse and solve real-world problems in various fields such as business, economics, and social sciences. E

*Remember (R), Understand (U), Apply (A), Analyse (An), Evaluate (E), Create (C)

Mapping of Course Outcomes to PSOs
PSO 1 PSO 2 PSO 3 PSO 4 PSO 5 PSO 6 PSO 7
CO 1 ✔ ✔ ✔ ✔
CO 2 ✔ ✔
CO 3 ✔ ✔ ✔ ✔
CO 4 ✔ ✔ ✔ ✔
CO 5 ✔ ✔ ✔
COURSE CONTENTS
Contents for Classroom Transaction
Module Description Hours Contents
1 Probability Theory 12
  1. Random experiment, definitions of probability (frequency, classical and axiomatic) addition theorem (2 and 3 events), numerical examples
  2. Conditional probability, multiplication theorem
  3. Independence of events: pair wise and mutual independence
  4. Baye's theorem and its applications
2 Random Variables 12
  1. Definition - discrete and continuous random variables
  2. Probability mass function and probability density function
  3. Distribution function - definition and properties
  4. Transformation of random variables - discrete and continuous
3 Bivariate Random Variables 12
  1. Definition of bivariate random variable
  2. Joint and marginal probability distributions
  3. Conditional distributions. Independence of random variables
4 Correlation and Regression Analysis 12
  1. Method of least squares - Fitting of linear and quadratic equations
  2. Correlation analysis – Definition and different types of correlation
  3. Methods of studying correlation: Scatter diagram, Karl Pearson correlation coefficient and its properties
  4. Simple linear regression: Fitting of regression lines, regression coefficients and their properties
5 Open End (Practical) 12 Numerical computation of concepts explained in Module 4 using MS Excel.
Essential Readings
  1. Gupta, S. C. & Kapoor, V. K. (1980). Fundamentals of Mathematical Statistics, Sultan Chand & Sons, New Delhi.
  2. Gupta, S. C. & Kapoor, V. K. (1994). Fundamentals of Applied Statistics, Sultan Chand & Sons, New Delhi.
  3. Gupta, S. P. (2004). Statistical Methods, Sultan Chand & Sons, New-Delhi.
Suggested Readings
  1. Mukhopadhyay, P. (1996). Mathematical Statistics, New Central Book Agency (P) Ltd., Kolkata.
  2. Agarwal, B. L. (2006). Basic Statistics, 4th Edition, New Age International (P) Ltd., New Delhi.
Assessment Rubrics
Evaluation Type Marks
End Semester Evaluation 70
Continuous Evaluation 30
a) Test Paper- 1 5
b) Test Paper-2 5
c) Assignment 10
d) Seminar -
e) Book/ Article Review -
f) Viva-Voce -
g) Field Report/Practical 10
Total 100