Course Archives    Theoretical Statistics and Mathematics Unit

Course: Probability Level: Postgraduate Time: Currently not offered

Syllabus Past Exams Syllabus 1. Concept of probability (8) Concept of random experiment with examples. Sample space and events. Basic properties with union and intersection of events. Classical definition of probability and its drawbacks. Axiomatic definition of probability, conditional probability, Bayes’ theorem, Independence of events, pair wise and mutual independence. 2. Concept of random variables and probability distributions (8) Discrete and continuous random variables, Probability mass function, Probability density function, Cumulative distribution function, Expectation, Variance, Moments, Moment generating function, Probability generating function, etc. 3. Discrete distributions (7) Binomial, Geometric, Negative Binomial, Poisson; Poisson approximation to Binomial distribution; moments- expectation and variance. Independence of discrete random variables. Distribution of the sum of two or more discrete independent random variables. 4. Continuous distributions (8) Uniform, Normal, Log-Normal, Exponential, Weibull and their moments; Independence of continuous random variables. Distribution of sum, product and ratio of two independent random variables. Some derived distributions such as χ2, t and Fdistributions. 5. Bivariate distribution (7) Joint probability distribution; Conditional distributions; covariance; correlation coeffcient; bivariate normal distribution 6. Limit Theorems (3) Chebyshev’s inequality, Weak law of large numbers (WLLN), Central limit theorem (Lindebergh & Levy). 7. Stochastic Process (9) Concept of Stochastic process, Markov Chains: Definition, Examples - Transition probability matrix - Chapman- Kolmogorov equation - classification of states - limiting and stationary distributions - ergodicity. Reference Texts: 1. Hoel, P. G., Port, S. C., & Stone, C. J. (1971). Introduction to probability theory. Houghton Mifflin. 2. Feller, W. (1957). An introduction to probability theory and its applications (Vol. 1). John Wiley & Sons. 3. Feller, W. (1966). An introduction to probability theory and its applications (Vol. 2). John Wiley & Sons. 4. Ross, S. M. (2005). A first course in probability. Prentice Hall 5. Karlin, S., & Taylor, H. M. (2014). A first course in stochastic processes. Academic Press. 6. Medhi, J. (2009). Stochastic processes (3rd ed.). New Age International. 7. Dobrow, R. P. (2016). Introduction to stochastic processes with R. Wiley. 8. Cinlar, E. (2013). Introduction to stochastic processes. Courier Corporation. Top of the page Past Exams

Top of the page

[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute]