416-3 - (d) If you win $1 each time head shows up and if...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Denker SPRING 2010 416 Stochastic Modeling - Assignment 3 Due date: Monday, 02/08/2010 in class Problem 1: (Problem 46, p.173) Show that Cov ( X, Y ) = Cov ( X, E [ Y | X ]) . Problem 2: (Problem 49, p. 174) A and B play a series of games with A winning each game with probability p . The overall winner is the Frst player to have won two more games than the other. (a) ±ind the probability that A is the overall winner. (b) ±ind the expected number of games played. Problem 3: (Problem 50, p. 174) There are three coins in a barrel. These coins ²ipped, will come up heads with respective probabilities 0 . 3, 0 . 5, and 0 . 7 respectively. A coin is randomly selected from among these three and is then ²ipped ten times. Let N be the number of heads on the ten ²ips. ±ind (a) P ( N = 0). (b) P ( N = n ) for n = 1 , 2 , 3 , ..., 10. (c) Does N have a binomial distribution?
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (d) If you win $1 each time head shows up and if you lose 1$ if tail shows up, are you playing a fair game? Explain your reasoning. Problem 4: (Problem 56, p.175) The number of daily accidents in a certain city is Poisson distributed. On a rainy day the parameter is = 0 . 8 and on a dry day it is = 0 . 2. Let X denote the number of accidents tomorrow, when it is predicted that it is a rainy day with probability 0 . 6. ind (a) E [ X ]. (b) P ( X = 0). (c) V ar ( X ). Problem 5: (Problem 57, p.175) The number of storms in an upcoming season is Poisson distributed with parameter which itself is random and has a uniform distribution over the interval (0 , 5). ind the probability that there are at least 3 storms this season....
View Full Document

Ask a homework question - tutors are online