Course Description
In this course, we discuss about standard Probability distributions and Random variables. Familiarity with Real analysis will be assumed.
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Course Content
1) Limits of sequences of sets, $\sigma$-field of events.
2) Probability measure, probability space.
3) Random variables, induced probability space, probability distribution. Distribution function of univariate random variables, decomposition theorem.
4) Discrete, continuous and absolutely continuous random variables. Examples. Distribution of functions of random variables.
5) Expectation, moments and moment generating function. Inequalities.
6) Multi-dimensional random variables (random vectors): Joint and marginal distribution functions. Independence. Moments and moment generating function.
7) Conditional distribution, conditional mean and conditional variance.
8) Multinomial and multivariate normal distributions.
9) Distribution of functions of random variables including Order statistics.
10) Properties of random vectors which are equal in distribution. Exchangeable random variables and their properties.
Course Audience
This is a compulsory course for M.Sc (Statistics) students. Students pursuing other degrees may take it as a Departmental/Open Elective.