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. .

TEXT:

D. Bertsekas and J. Tsitsiklis, Introduction to Probability, 2nd ed, Athena Scientific, 2008.

REFERENCES:

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.