UNIT – I: PROBABILITY THEORY AND DISTRIBUTIONS
Sample space and events, Probability measures and probability space-Random
variables, Discrete and Continuous random variable, probability density and
distribution functions. Simple theorems on Probability. Marginal and conditional
distribution, Expectations and moments, Independence of events, Moments and
Cumulants generating functions.
Discrete Uniform Binomial, Multinomial, Poisson, Negative – Binomial,
Hypergeometric Distributions. Uniform, Normal, Cauchy, Beta, Gamma, Log Normal,
Exponential, Weibull distributions, Chi square, t and F distributions.
UNIT – II: STATISTICS INFERENCE
Point estimation – Interval estimation – Properties of estimate – consistency,
Unbiasedness efficiency sufficiency and Completeness, Fisher – Neyman
Factorisation and Rao –A Blackwell Theorems, Lehman – Scheffe theorem, Cramer –
Rae inequality, method of maximum likelihood estimate and its properties, method of
moments, method of minimum chi-square.
Simple and Composite Hypothesis, two kinds of error, power functions, most
powerful test, Neyman – Pearson Lemma UMP and unbiased test, MLR property
and its use for construction of UMP tests, Likelihood ratio test, confidence intervals
for large and small samples.
Run test for Randomness, Median test, sign test for location, Wilcoxon – Mann
Whitney U – test and Kolmogrov – Smirnov tests