Probability Distributions

Paper Code: 
STT-201
Credits: 
3
Contact Hours: 
45.00
Max. Marks: 
100.00
Objective: 

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

Course

Learning outcomes (at course level

Learning and teaching strategies

Assessment Strategies

 

Paper Code

Paper Title

STT-201

Probability Distributions

CO 14: Able to understand the concept of random variable and their expectations.

 

CO 15: Able to obtain the moments from moment generating function of various discrete and continuous distribution which helps them to study the population deeply.

 

CO 16: Able to identify the behaviour of the population.

 

CO 17: Gaining knowledge about how to derive the probability distribution function of random variables.

 

CO 18: Analyse the behaviour of the data by Fitting discrete and continuous distributions.

Approach in teaching:

 

Interactive Lectures,

Group Discussion,

Classroom Assignment

Problem Solving Sessions

 

Learning activities for the students:

 

Assignments

Seminar

Presentation

Subject based  Activities

 

Classroom Quiz

Assignments

Class Test

Individual Presentation

 

9.00
Unit I: 
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. Chebychev’s inequality with simple applications. Central moments and Non-central moments, Moment generating functions and their properties. Cumulant generating functions.

9.00
Unit III: 
Basic Distributions:

Bernoulli, Binomial, Poisson, Normal distribution with properties and examples. Fitting of Binomial and Poisson distribution and Normal distribution.

 

9.00
Unit IV: 
Univariate Discrete Distribution:

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

9.00
Unit V: 
Univariate Continuous Distribution:

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

 

Essential Readings: 

1. Goon, A.M., Gupta, M.K. and Gupta, B. Das (1991): Outline of Statistics, Volume I, 

    The World Press PvtLtd , Calcutta            

2. Gupta, S.C. and Kapoor ,V.K.: (2000) Fundamentals of Mathematical Statistics, S Chand & Company, New Delhi

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

 

References: 

1. Mood Alexander M., GraybillFrankline and Boes Duane C.:(2007) Introduction to Theory

    of Statistics, McGraw 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.: (2005) Univariate Discrete

    Distributions, Second Edition.

 

Academic Year: 
2020-2021
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