Math 505b: Applied Probability
Monday-Wednesday-Friday, 1-1.50pm, in KAP 148
Textbook: Gimmett and Stirzaker: Probability & Random Processes (3rd).
Grader: Jia Zhuo, email@example.com, KAP 248A
Review session: Friday, May 2nd, 1pm-1:50pm KAP 148, then 2pm-3:20pm KAP 163.
|Homework #1||Wed. January 29th||HW1.pdf||HW1.Solution.pdf|
|Homework #2||Wed. February 19th||HW2.pdf||HW2.Solution.pdf|
|Homework #3||Wed. February 26th||HW3.pdf||HW3.Solution.pdf|
|Homework #4||Wed. March 5th||HW4.pdf||HW4.Solution.pdf|
|Homework #5||Wed. March 26th||HW5.pdf||HW5.Solution.pdf|
|Homework #6||Mon. April 7th||HW6.pdf||HW6.Solution.pdf|
A collection of problems:
Practice Problems, week 1 p170: 2, 4, 5
Practice problem, week 2 Random walks: prove that the probability that the random walk stays non-negative up to time 2n is the same as the probability that the random walk is equal to 0 at time 2nBallot Theorem: Suppose that in an election, candidate A receives a votes and candidate B receives b votes. A wins over B (a>b). Assuming random ordering of the votes, what is the probability that A is always ahead of B in the vote count?
Practice problem, week 3 p219: 1, 2, 3, 6check properties (2) and (3) p214 in the book.p223: 2, 5
Practice problem, week 4 p225, Example (6)p225: 1, 3, 4
Practice problem, week 5 p236: 3, 4, 6, 11
Practice problems, week 6 Problems on Markov Chains (sheet of problems given above): pb 4, 6, 7, 8, 9, 13
Practice problems, week 8 p475: 1, 4, 5Show that the Wright-Fisher model (HW2) is a martingale. Deduce the probability that allele A wins over allele B, from the (not yet) non-rigorous De Moivre's approach (seen in class).
Practice problems, April 2nd p495: 4, 7, 8
Practice problems, April 9th p508: 1, 6, 7, 8, 13
- Quentin Berger
- USC, Department of Mathematics
- 3620 S. Vermont Ave, KAP 108
- Los Angeles, California 90089-2532
- Phone: (213) 821 - 1628
- Email: firstname.lastname@example.org