UNIT–I
Discrete Distributions – 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 Distributions – 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: 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: Rectangular, 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.