MA2040 Probability, Stochastic Process and Statistics


Course Details

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. .


Course References:

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.