Probability: Probability spaces, random variables and random vectors, functions of random vectors, univariate and multivariate distributions, mathematical expectations, moment generating functions, convergence in probability and in distribution and related results; Sampling distributions.
Statistics: Point estimation - estimators, sufficiency, completeness, minimum variance unbiased estimation, maximum likelihood estimation, method of moments, Cramer-Rao inequality, consistency; Interval estimation; Testing of hypotheses - tests and critical regions, Neymann-Pearson lemma, uniformly most powerful tests, likelihood ratio tests; Correlation and linear regression.
Weights in different examinations are as follows:
For each examination, linear scaling will be used (if needed).
An F grade will be awarded if you obtain less than 20% of total marks after the end semester examination.