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Indian Institute of Science Education and Research Berhampur

MTH 310: Introduction to probability theory (4)

Prerequisites: NIL

Course contents:

Probability: Classical, relative frequency and axiomatic definitions of probability, addition rule and conditional probability, total probability, Bayes Theorem and independence, equally likely experiments, coin tossing and random walk. Random Variables: Discrete, continuous and mixed random variables, probability mass, probability density and cumulative distribution functions, mathematical expectation, moments, probability and moment generating function, median and quantiles, Markov inequality, Chebyshev’s inequality,weak law of large numbers and central limit theorem. Special Distributions (Binomial, Poisson, Normal), Joint Distributions: Joint, marginal and conditional distributions. Joint distributions of independent random variables and applications to find the sum, product and ratio of random variables. Transformations, generating functions, convolution and its connection with probability distributions.
Random walk: Reflection principle.
Markov chain: Connection with random walk. Recurrence and transience.
Stationary distribution (if time permits).

Suggested Books:

• W. Feller: Introduction to the Theory of Probability and its Applications, (Vols. 1 & 2).
• K. L. Chung: Elementary Probability Theory.
• S. M. Ross: A First Course in Probability.

References:

• R. Ash: Basic Probability Theory.
• P. G. Hoel, S. C. Port and C. J. Stone: Introduction to Probability Theory.

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