MA2201 : Probability and Statistics (Spring 2015) | Academic Portal of IISER Kolkata

Details of MA2201 (Spring 2015)

Level: 2

Type: Theory

Credits: 3.0

Course Code	Course Name	Instructor(s)
MA2201	Probability and Statistics	Buddhananda Banerjee

Syllabus
Probability : Classical definition, and problems solved by elementary combinatorial methods; 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/ 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 to binomial/ central limit theorem in iid case); joint distribution of two random variables (with more emphasis on the discrete case); ideas of conditional expectation and variance. Statistics : Correlation and regression; simple random sampling with and without replacement, expectation and standard error of the sample mean and the sample proportion; maximum likelihood estimation; introduction to confidence intervals; concept of testing of hypothesis, notion of Type I and Type II errors, tests for mean and variance in one and two-sample cases, tests related to regression problems, test for population proportion.

Syllabus

Probability : Classical definition, and problems solved by elementary combinatorial methods; 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/ 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 to binomial/ central limit theorem in iid case); joint distribution of two random variables (with more emphasis on the discrete case); ideas of conditional expectation and variance.
Statistics : Correlation and regression; simple random sampling with and without replacement, expectation and standard error of the sample mean and the sample proportion; maximum likelihood estimation; introduction to confidence intervals; concept of testing of hypothesis, notion of Type I and Type II errors, tests for mean and variance in one and two-sample cases, tests related to regression problems, test for population proportion.

References
G. Casella and R. L. Berger, Statistical Inference, Thomson Brooks / Cole, 2002. P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Probability Theory, Thomson Brooks / Cole, 1972. N. Pal and S. Sarkar, Statistics : Concepts and Applications, Prentice Hall, 2005. S. Ross, First Course in Probability, (8th Edition), Prentice-Hall, 2009.

Sl. No.	Programme	Semester No	Course Choice
1	IP	2	Not Allowed
2	IP	4	Not Allowed
3	MR	2	Not Allowed
4	MR	4	Not Allowed
5	MS ( Mathematical Sciences )	4	Core
6	RS	1	Elective
7	RS	2	Not Allowed