Probability Distributions

Paper Code: 
STT 201
Credits: 
3
Contact Hours: 
46.00
Max. Marks: 
100.00
Objective: 

This paper is aimed at teaching the students various probability distributions which are useful in day to day life.

8.00
Unit I: 
Random Variable

Random Variable: Definition and types of random variables. Probability mass function and Probability density function. Distribution function with properties (without proof). Joint, Marginal and Conditional probability distributions. Independence of two variable, definition and application of Jacobian transformation for one and two variables.

9.00
Unit II: 
Mathematical Expectations

Expectation of a random variable and its simple properties. Addition and Multiplication theorems of Expectations. Variance and covariance and their properties.

8.00

Chebychev’s inequality with simple applications. Central moments and Non-central moments, Moment generating functions and their properties. Cumulant generating functions.

10.00
Unit IV: 
Univariate Discrete Distribution

Bernoulli, Binomial, Poisson, Geometric Distribution with simple properties and applications. Fitting of Binomial and Poisson Distribution. Hypergeometric and Negative Binomial Distribution (examples, derivations, mean and variance) .

10.00
Unit V: 
Univariate Continuous Distribution

Rectangular, Normal, Exponential, Cauchy, Gamma, Beta Distribution with properties. Bivariate normal distribution and its pdf without proof.

Essential Readings: 

1. Goon, A.M., Gupta, M.K. and Gupta, B. Das (1991): Outline of Statistics, Volume I, The World Press Pvt Ltd , Calcutta

2. Gupta, S.C. and Kapoor ,V.K.: Fundamentals of Mathematical Statistics, S Chand & Company, New Delhi

3. Gupta, O.P.:Mathematical Statistics, Kedarnath Publication, Meerut.

References: 

1. Mood Alexander M., Graybill Frankline and Boes Duane C.: Introduction to Theory of Statistics, Mc Graw Hill & Company Third Edition

2. Paul Mayor L. (1970): Introductory Probability and Statistical Application, Oxford & IBM Publishing Company Pvt Ltd, Second Edition.

3. Yule Udny G., and Kendall,M.G. (1999): An Introduction to the theory of Statistics, 14th Edition

4. Speigel M.R., (1967): Theory and Problem of Statistics, Schaum’s Series.

5. Johnson Norman L., Kotz Samuel and Kemp Adriene W.: Univariate Discrete Distributions, Second Edition.

Academic Year: 
2019-2020
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