SECOND SEMESTER STATISTICS
PROBABILITY THEORY AND DISTRIBUTIONS
UNIT-I
Introduction to Probability: Basic Concepts of Probability, random experiments, trial, outcome, sample space, event, mutually exclusive and exhaustive events, equally likely and favourable outcomes. Mathematical, Statistical, axiomatic definitions of probability. Conditional Probability and independence of events, Addition and multiplication theorems of probability for 2 and for n events. Boole's inequality and Baye's theorem and its applications in real life problems.
UNIT-II
Random variable: Definition of random variable, discrete and continuous random variables, functions of random variable. Probability mass function. Probability density function, Distribution function and its properties. For given pmf, pdf calculation of moments, coefficient of skewness and kurtosis. Bivariate random variable - meaning,joint, marginal and conditional Distributions, independence of random variables andsimple problems.
UNIT- III
Mathematical expectation : Mathematical expectation of a random variable and function of a random variable. Moments and covariance using mathematical expectation with examples. Addition and Multiplication theorems on expectation. Definitions of M.G.F, C.G.F, P.G.F, C.F and their properties. Chebyshev and Cauchy - Schwartz inequalities.
UNIT-IV
Discrete Distributions: Binomial, Poisson, Negative Binomial, Geometric distributions:Definitions, means, variances, M.G.F, C.F, C.G.F, P.G.F, additive property if exists. Possion approximation to Binomial distribution. Hyper-geometric distribution: Definition, mean and variance.
UNIT - V
Continuous Distributions: Rectangular, Exponential, Gamma, Beta Distributions: mean variance, M.G.F, C.G.F, C.F.Normal Distribution: Definition, Importance, Properties,,