##
Applied Probability (ACMS 60850): Qualifying Exam Guide

** Textbook:** "Probability and Random Processes" by Grimmett and Stirzaker,
Third edition 2009, Oxford Univ Press, ISBN 978-019-857222-0.

** Syllabus:**
You are responsible for these materials:

- Basic setup of probability theory (including sample spaces, conditional
probability, independence). Random variables (including the elements of
measure and integration theory).
- Discrete random variables (including random walks).
- Continuous random variables, the basic distributions, sums of random variables.
- Monte Carlo simulations.
- Generating functions, branching processes, basic theory of characteristic
functions.
- Laws of large numbers, central limit theorems.
- Markov chains (embedding, birth and death processes, Poisson processes)
- Convergence of random variables (convergence in distribution, probability, mean-square, almost surely).
- Various stochastic processes, including Brownian motion, and applications.
- Martingales (discrete version only), including stopping times and optimal stopping.
- The rudiments of stochastic integration (including Ito's formula and the
Black-Scholes differential equation).

**Here are sample exams:**

- 2020 Qualifying Exam in Probability (3 hours).
- 2020 Qualifying Exam answers (DO NOT read until you try the exam first).
- 2018 Qualifying Exam in Probability (3 hours).
- 2018 Qualifying Exam answers (DO NOT read until you try the exam first).
- 2017 Qualifying Exam in Probability (3 hours).
- 2017 Qualifying Exam answers (DO NOT read until you try the exam first).
- A sample midterm exam (90 minutes).
- Midterm exam answers.
- A sample final exam (2016 Fall take home).
- Final exam answers (2016 Fall take home).
- A sample final exam (2017 Fall take home).
- Final exam answers (2017 Fall take home).

**ACMS 60850:**

- Course webpage (2017)