exam2 - Math 4740 Exam 2, March 30, 2009 R. Durrett 1. (21...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 4740 Exam 2, March 30, 2009 R. Durrett 1. (21 points) Let Y 1 ,Y 2 ,... be independent with P ( Y i = 2) = p and P ( Y i = 1 / 2) = 1- p . Let X n = X Y 1 Y n and think of X n as the price of a stock at time n . (a) What choice of p makes X n a martingale? We will use this value of p for the rest of the problem, and suppose X = 1. (b) Find lim n (1 /n ) log 2 X n (log base 2) and conclude X n 0. (c) Find P ( T 4 < ) where T 4 = min { n 0 : X n = 4 } . 2. (20 points) When Chad arrives at the bank, Al and Bob are being served by tellers 1 and 2, who have exponential service times with means 4 and 2 minutes. When the first service is complete Chad goes to the teller that is free. (a) Find the probabilities that Al, Bob and Chad are the last to leave. (b) What is the expected time Chad is at the bank (waiting plus service time)? 3. (39 points) A policewoman on the evening shift writes a Poisson mean 6 number of tickets per hour. 2/3s of these are for speeding and cost $100....
View Full Document

Page1 / 3

exam2 - Math 4740 Exam 2, March 30, 2009 R. Durrett 1. (21...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online