MA2040 Probability, Stochastic Process and Statistics
Probability: Probability models and axioms, conditioning and Bayes' rule, independence discrete random variables; probability mass functions; expectations, examples, multiple discrete random variables: joint PMFs, expectations, conditioning, independence, continuous random variables, probability density functions, expectations, examples, multiple continuous random variables, continuous Bayes rule, derived distributions; convolution; covariance and correlation, iterated expectations, sum of a random number of random variables.
Stochastic process: Bernoulli process, Poisson process, Markov chains. Weak law of large umbers, central limit theorem.
Statistics: Bayesian statistical inference, point estimators, parameter estimators, test of hypotheses, tests of significance. .
D. Bertsekas and J. Tsitsiklis, Introduction to Probability, 2nd ed, Athena Scientific, 2008.
1. K.L. Chung, Elementary Probability Theory with Stochastic Process, Springer Verlag, 1974.
2. A. Drake, Fundamentals of Applied Probability Theory. McGraw-Hill, 1967.
3. O. Ibe, Fundamentals of Applied Probability and Random Processes.Academic Press, 2005.
4. S. Ross, A First Course in Probability. 8th ed. Prentice Hall, 2009.