MA2202 : Probability I (Spring 2018) | Academic Portal of IISER Kolkata

Details of MA2202 (Spring 2018)

Level: 2

Type: Theory

Credits: 3.0

Course Code	Course Name	Instructor(s)
MA2202	Probability I	Asok Kumar Nanda

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. Markov Chain : Discrete state space, discrete time, Chapman-Kolmogorov equations, classification of states, limiting probabilities.

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.
Markov Chain : Discrete state space, discrete time, Chapman-Kolmogorov equations, classification of states, limiting probabilities.

References
Cacoullos, T., Exercises in Probability, Springer. Feller, W., An Introduction to Probability Theory and Its Applications, Vol. I, Wiley. Gupta, S. C. and Kapoor, V. K., Fundamentals of Mathematical Statistics, S. Chand. Hoel, P. G., Port, S. C. and Stone C. J., Introduction to Probability Theory, Thomson Brooks / Cole. Ross, S., introduction to Probability Models, Prentice-Hall. Miller, I. and Miller, John E. Freud's Mathematical Statistics with Applications, Pearson. --

References

Cacoullos, T., Exercises in Probability, Springer.
Feller, W., An Introduction to Probability Theory and Its Applications, Vol. I, Wiley.
Gupta, S. C. and Kapoor, V. K., Fundamentals of Mathematical Statistics, S. Chand.
Hoel, P. G., Port, S. C. and Stone C. J., Introduction to Probability Theory, Thomson Brooks / Cole.
Ross, S., introduction to Probability Models, Prentice-Hall.
Miller, I. and Miller, John E. Freud's Mathematical Statistics with Applications, Pearson.

Sl. No.	Programme	Semester No	Course 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