This course will focus on mathematical methods for statistical inference, which include:

1. A Review of  probability distributions and their properties.

2. Theory of estimation: Estimation of a parameter, criteria of a good estimator – unbiasedness, consistency, efficiency, &sufficiency and. Statement of Neyman's factorization theorem. Estimation of parameters by the method of moments and maximum likelihood (M.L), properties of MLE’s. Binomial, Poisson &Normal Population parameters estimate by MLE method.

3.Testing of Hypothesis: Concepts of statistical hypotheses, null and alternative hypothesis, critical region, two types of errors, level of significance and power of a test. One and two tailed tests. Neyman-Pearson’s lemma. Examples in case of Binomial, Poisson, Exponential and Normal distributions.