## Details of MA2202 (Spring 2020)

 Level: 2 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
MA2202 Probability I Asok Kumar Nanda

Syllabus
Probability: Classical definition, frequency definition and set theoretic definition of probability
for discrete sample spaces, basic probability theorems (union of events/Booles inequality, etc.),
independence of events, conditional probability, Bayes theorem, discrete probability
distributions (binomial, Poisson, hypergeometric, geometric, negative binomial), continuous
probability distributions (exponential, uniform, normal), moments and moment generating
function, basic limit theorems (Chebyshevs inequality, weak law of large numbers, normal
approximation of binomial, central limit theorem in iid case), joint distribution of two random
variables (with emphasis on the discrete case), notions of conditional expectation and variance,
maximum and minimum order statistics.
Markov Chain: Discrete state space, discrete time, Chapman-Kolmogorov equations,
classification of states, limiting probabilities.

References
1. Cacoullos, T., Exercises in Probability, Springer.
2. Feller, W., An Introduction to Probability Theory and Its Applications, Vol. I, Wiley.
3. Gupta, S.C. and Kapoor, V.K., Fundamentals of Mathematical Statistics, S. Chand.
4. Hoel, P.G., Port, S.C. and Stone, C.J., Introduction to Probability Theory, Thomson
Brooks/Cole.
5. Ross, S., Introduction to Probability Models, Prentice-Hall.
6. Miller, I. and Miller, M., John E. Freunds Mathematical Statistics with Applications, Pearson.

#### Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 2 Not Allowed
2 IP 4 Not Allowed
3 IP 6 Not Allowed
4 MR 2 Not Allowed
5 MR 4 Not Allowed
6 MS 4 Core
7 RS 1 Not Allowed
8 RS 2 Not Allowed