Course policy

Reference texts:

Robert B. Ash: Basic probability Theory

Rohatgi and Saleh: Mathematical Statistics

Kai Lai Chung: Probability Theory

Billingsley: Measure and probability

Feller: An introduction to Probability Theory and its applications (Volume I and Volume II)

Athreya and Lahiri: Measure theory and probability theory

Syllabus:

1. Axiomatic definition of probability.

2. Random variables and random vectors.

3. Conditional probabilities and densities.

4. Expectation, moments and generating functions.

5. Functions of random vectors. Sampling distribution. Multivariate Gaussian random variables and quadratic forms.

6. Probability inequalities and moment inequalities.

7. More on sigma-algebra and measurable functions. Almost sure convergence. MCT and DCT.

8. Convergence of random variables.

Evaluation scheme for the course:

Assignment 15%

Quiz 15% (Best 2 out of 3)

Midsem 30%

Endsem 40%

Grading is relative.