PROBABILITY AND STATISTICS
Probability and Statistics or also called Statistics and Probability are two related but separate academic disciplines. Statistical analysis often uses probability distributions, and the two topics are often studied together. However, probability theory contains much that is mostly of mathematical interest and not directly relevant to statistics. Moreover, many topics in statistics are independent of probability theory.
Unit I Basics of Probability : Sample Space and Events, Probability of an Event, Rules of Probability, Conditional Probability and Independent Events
Unit II Random variables and its Characterization : Random Variable ( Discrete and Continuous ), Expectation and Variance of a Random Variable, Moments and Moment generating functions, Characteristic functions
Unit III Probability Distributions and Regression : Linear Regression, Binomial Distribution, Poisson Distribution, Normal Distribution
Unit IV Point Estimation : Definition ,Unbiased Estimators, Consistent Estimators, Sufficient Estimator, MLE ( Method of Maximum Liklihood ) Unit V Limit Theorem , Convergence and Stochastic Process : Limit Theorems, Convergence of Random Variables, Stochastic processes, Elementary concept related to Markov chains
Unit VI Hypothesis Testing : Types of Error, Student t-test, Chi- Square Test, Goodness of a Fit
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