Code for branching processes: branching_proc.R
Code for the Polya urn scheme: polya.R
We shuffle a deck by the following method:
Take the top card off the top of the deck and place back into the deck in a position chosen uniformly at random.
It is allowable that the top card will be put directly on top again.
Let denote the position of the Queen of Hearts at time . We assume that the Queen of Hearts starts on top, i.e. , and wish to compute the expected time for it to return to the top.
The probability transition matrix when there are a total of FIVE cards is:
What is the expected time until the shuffler sees the Queen of Hearts on top of the deck when there are 52 cards?
You may use the book, but you may not communicate with other students on this problem. Work smart! The solution does not require solving a 52-dimensional system of equations. (Hint: It may help to solve the 5-card case first and then attack the larger problem.)
This is your reminder that the course midterm is coming up soon. It will be in-class and closed book (and closed notes). You will not be allowed to use a calculator.
The midterm material will include everything we have covered in class from Durrett, Chapter 1.
Definitions, Statements of Theorems, Examples, Counterexamples: 50%.
Problem Solving: 50%
Bayesian Inference and MCMC methods, Math 7770
MWF 1:00 – 1:50 pm, Gibson 308
Office Hours, Gibson 427
Thu 10:00 am – 12:00 pm; Fri 11:00 am – noon.
Large Deviations Learning Group
Mon 3:00 – 3:50 pm
The Tulane Probability and Statistics Seminar
Wed 3:00 – 4:00 pm, Gibson Hall 414
6823 St Charles Ave
New Orleans, LA 70118
Phone: (504) 862-3426