Module-1: Probability Distributions

Probability Distributions: Review of basic probability theory. Random variables (discrete
and continuous), probability mass and density functions. Mathematical expectation, mean and
variance. Binomial, Poisson and normal distributions- problems (derivations for mean and
standard deviation for Binomial and Poisson distributions only)-Illustrative examples.
Exponential distribution.

Module-2: Joint probability distribution & Markov Chain

Joint probability distribution: Joint Probability distribution for two discrete random
variables, expectation, covariance and correlation.
Markov Chain: Introduction to Stochastic Process, Probability Vectors, Stochastic matrices,
Regular stochastic matrices, Markov chains, Higher transition probabilities, Stationary
distribution of Regular Markov chains and absorbing states.

Module-3: Statistical Inference 1

Introduction, sampling distribution, standard error, testing of hypothesis, levels of significance,
test of significances, confidence limits, simple sampling of attributes, test of significance for
large samples, comparison of large samples.

Module-4: Statistical Inference 2

Sampling variables, central limit theorem and confidences limit for unknown mean. Test of
Significance for means of two small samples, students ‘t’ distribution, Chi-square distribution
as a test of goodness of fit. F-Distribution.

Module-5: Design of Experiments & ANOVA

Principles of experimentation in design, Analysis of completely randomized design,
randomized block design. The ANOVA Technique, Basic Principle of ANOVA, One-way
ANOVA, Two-way ANOVA, Latin-square Design, and Analysis of Co-Variance