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SYLLABUS

UNIT - I

Discrete Distribution – I: Uniform and Bernoulli Distributions: Definitions, Mean, Variance and Simple Examples. Definition and Derivation of Probability Mass Functions of Binomial Distribution, Poisson Distribution, Properties of these Distributions: Median, Mode, m.g.f, c.g.f, p.g.f, c.f., and Moments upto Fourth Order, Reproductive Property (wherever exists) and their Real Life Applications. Poisson Approximation to Binomial Distribution.

UNIT - II

Discrete Distribution – II: Negative Binomial, Geometric Distributions: Definitions and Real Life Applications, Properties of these Distributions: m.g.f, c.g.f., p.g.f., c.f. and Moments upto Fourth Order, Reproductive Property (wherever exists), Lack of Memory Property for Geometric Distribution. Poisson Approximation to Negative Binomial Distribution. Hyper-geometric Distribution: Definition, Real Life Applications, Derivation of Probability Function, Mean, Variance. Binomial Approximation to Hyper-geometric Distribution.

UNIT - III

Continuous Distributions – I: Rectangular and Normal Distributions – Definition, Properties such as m.g.f., c.g.f., c.f. and Moments up to Fourth Order, Reproductive Property, Wherever Exists and their Real Life Applications. Normal Distribution as a Limiting Case of Binomial and Poisson Distributions.

UNIT - IV

Continuous Distributions – II: Exponential, Gamma Distributions – Definition, Properties: m.g.f., c.g.f., c.f. and Moments upto Fourth Order, Reproductive Property (wherever exists) and their Real Life Applications. Beta Distribution of Two Kinds: Definitions, Mean and Variance. Cauchy Distribution – Definition and c.f. Definition of Convergence in Law, in Probability and with Probability One or Almost Sure Convergence. Definition of Weak Law of Large Number (WLLN) and Strong Law of Large Numbers (SLLN). Definition of Central Limit Theorem (CLT) for Identically and Independently Distributed (i.i.d) Random Variables with Finite Variance.