Home /  Departments /  Aided /  Under Graduate /  Statistics /  Data Analysis

SEMESTER III

B9 – DISCIPLINE SPECIFIC MINOR COURSE
KU3DSCSTA221: PROBABILITY DISTRIBUTIONS
Semester Course Type Course Level Course Code Credits Total Hours
III MINOR 200 – 299 KU3DSCSTA221 4 75

Learning Approach (Hours/Week) / Marks Distribution
Lecture Practical/Internship Tutorial CE ESE Total Duration of ESE (Hours)
3 2 - 35 65 100 1½
Course Description

This course provides a comprehensive study of mathematical expectation, including properties, addition and multiplication theorems, moments, and extends to bivariate random variables, discrete distributions such as uniform, binomial, Poisson, and geometric, and continuous distributions like rectangular, exponential, and normal distributions.

Course Prerequisite

Foundation Courses (Level 100 – 199)

Course Outcomes
CO No. Expected Outcome Learning Domains
1 Students will understand the definition and properties of mathematical expectation, including linearity and additivity. U
2 Students will be able to calculate conditional means and variances for bivariate random variables. A
3 Students will understand various discrete probability distributions, including uniform, binomial, Poisson, and geometric distributions. R
4 Students will learn about common continuous probability distributions, such as rectangular, exponential, and normal distributions. R
5 Students will gain practical skills in using spreadsheets to perform calculations related to diagrams, graphs, measures of central tendency, dispersion, moments, correlation, regression, and probability. E
COURSE CONTENTS
Contents for Classroom Transaction
Module Description Hours Contents
1 Mathematical Expectation 11
  1. Definition and properties of mathematical expectation
  2. Addition and multiplication theorem on expectation
  3. Expectation of functions of random variables
  4. Moments - Definition of raw and central moments, relation between raw and central moments
2 Expectation of Bivariate Random Variables 10
  1. Conditional mean and variance
  2. Coefficient of correlation between random variable
  3. Moment generating function - Definition and properties
  4. Characteristic function - Definition and properties
3 Discrete Distributions 12
  1. Uniform Distribution: Definition, mean variance and mgf, simple problems
  2. Binomial: Definition, mean variance and mgf, simple problems
  3. Poisson: Definition, mean variance and mgf, simple problems
  4. Geometric: Definition, mean, variance and mgf, lack of memory property
4 Continuous Distributions 12
  1. Rectangular distribution: Definition, mean variance and mgf, simple problems
  2. Exponential distribution: Definition, mean variance and mgf, simple problems
  3. Normal distribution: Definition, mean variance and mgf, simple problems
  4. Standard normal distribution: Definition, mean variance and mgf, simple problems
5 Open End (Practical) 30 Numerical computation of the above concepts.
Essential Readings
  1. Gupta, S. C. & Kapoor, V. K. (1980). Fundamentals of Mathematical Statistics, Sultan Chand & Sons, New Delhi.
  2. Goon, A. M., Gupta, M. K. & Dasgupta, B. (2003). An Outline of Statistical Theory, Volume I, 4th Edn, The World Press Pvt. Ltd., Kolkata.
Suggested Readings
  1. John E. Freund (1980). Mathematical Statistics, Prentice Hall of India, New Delhi.
  2. Rohatgi, V. K. (1993). An Introduction to Probability Theory and Mathematical Statistics, Wiley Eastern, New Delhi.
  3. Mood, A. M., Graybill, F. A. & Bose, D. C. (2007). Introduction to the Theory of Statistics, 3rd Edn (Reprint). Tata McGraw-Hill Publishing Company 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