Module 1: Probability Distributions Random variables (discrete and continuous), probability mass/density functions. Binomial, Poisson, Normal, and Exponential distributions.
Module 2: Joint Probability Distribution & Markov Chains Two-dimensional random variables, covariance, and correlation. Stochastic processes, transition probabilities, and stationary distributions.
Module 3: Statistical Inference I Sampling distributions, standard error, and hypothesis testing. Confidence limits and large sample tests.
Module 4: Statistical Inference II Central Limit Theorem and small sample tests (Student’s t-distribution). Chi-square distribution for goodness of fit and F-distribution.
Module 5: Design of Experiments & ANOVA Principles of experimentation and Analysis of Variance (One-way and Two-way ANOVA). Latin-square Design and Analysis of Co-Variance.