Slot - G (Tues, Wed, Fri 12:00-12:55)
Venue - B-LH2, IIT Hyderabad
Syllabus -
Basic probability: Sample space and events, definitions of probability, properties of probability, conditional probability.
Random variables: distribution functions, discrete and continuous random variables, moments of random variables, independence, conditional expectation, functions of random variables, covariance.
Special Distributions: Bernoulli, Binomial, Geometric, Poisson, Exponential, Uniform, Normal distribution.
Inequalities: Markov's, Chebyshev's, Jensen's, Minskowski', Chernoff bounds.
Stochastic process: Markov chain, birth and death process, random walk.
Convergence of random variables - weak, in probability and almost sure, central limit theorem, weak law of large numbers, limsup and liminf of events, Borel-Cantelli lemma and strong law of large numbers.