Syllabus for Probability Qualifying Exam

The Probability exam covers essentially the material taught in MTH G241 (Probability 1).

Topics

• Probability distributions, joint distributions, expectations and conditional expectations.
• Convergence in distribution of sums of i.i.d. random variables (the law of large numbers, the central limit theorem) and convergence in distribution of maxima and minima of i.i.d. random variables.
• Markov chains. Classification of states. Equations for the stationary distribution of recurrent classes and the limit of the n-th power of the transition matrix. Time reversible chains. Branching processes.
• Random walks on the integers and difference equations for hitting time probabilities and expected time to boundaries.

References

• Sheldon M. Ross, Introduction to Probability Models, 8th edition, Academic Press, 2002.
• Geoffrey Grimmett and David Stirzaker, Probability and Random Processes, Oxford University Press, 3rd edition, 2001.