Probability, Statistics and Stochastic Processes, Jul-Nov 2021


Sivaram Ambikasaran,


Probability Axiomatic definition of probability, Independent Events, Baye's theorem, Discrete and continuous random variables, Distribution, Functions of random variables, Expectation, Variance, Correlation coefficient, Chebyshev’s inequality, Markov inequality, Conditional expectations, Standard discrete and continuous distributions (Binomial, Poisson, Geometric, Exponential, Normal, Chi-square), Moment generating function, Sums of random variables, Law of large numbers, Central limit theorem, Normal approximation to Binomial.
Statistics Sampling distribution, Estimation of parameters, Maximum likelihood estimates, Confidence intervals, Student’s t-distribution, Testing hypothesis, Goodness of fit.
Stochastic Processes Discrete random process, Stationary random process, Bernoulli process, Poisson process, Markov chain.


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