Problem Set 5
Math 430/AMCS 530
Solutions are to be placed in my mailbox in DRL 4W1 by 5pm on 29 October, 2010.
(10 pts)
(1)
On average, only one person in a thousand has a particular rare blood type.
Recall that we dened fkj as the probability of a state sj ever entering a state sk in a Markov
chain. We then used it to dene persistent and transient states:
Denition 0.1. A state si with fii = 1 is
Consider a collection of random variables cfw_Xi for 1 i n, with the same sample
space : that is,
Xi : R0 .
We can consider measuring all of these for a given outcome, whereupon we obtain
a collectio
Problem Set 8
Math 430/AMCS 530
Solutions are to be placed in my mailbox in DRL 4W1 by 5pm on 3 December, 2010.
(10 pts)
(1) Let (S, P ) be a Markov chain, with random variables Xi representing the st
Problem Set 7
Math 430/AMCS 530
Solutions are to be placed in my mailbox in DRL 4W1 by 5pm on 19 November, 2010.
(5 pts)
(1) Consider a BTP with 48 trials and probability 3/4 of success. Using the nor
Problem Set 6
Math 430/AMCS 530
Solutions are to be placed in my mailbox in DRL 4W1 by 5pm on 5 November, 2010.
(10 pts)
(1)
Consider an n-step Bernoulli trials process. Show that if U is a random var
Problem Set 4
Math 430/AMCS 530
Solutions are to be placed in my mailbox in DRL 4W1 by 5pm on 22 October, 2010.
(5 pts)
(1)
A high-school has 3000 students. Consider subsets of size 100 chosen by the
Problem Set 3
Math 430/AMCS 530
Solutions are to be placed in my mailbox in DRL 4W1 by 5pm on 15 October, 2010.
(5 pts)
(1)
Let E, F be events with positive probability of occuring, but simultaneously
Problem Set 2
Math 430/AMCS 530
Solutions are to be placed in my mailbox in DRL 4W1 by 5pm on 1 October, 2010.
(10 pts)
(1)
()
We extend the denition of the binomial coecient n to arbitrary real numbe
Problem Set 1
Math 430/AMCS 530
Solutions are to be placed in my mailbox in DRL 4W1 by 5pm on 24 September, 2010.
(10 pts)
(1) Let A, B, C be arbitrary sets. Verify the following equalities
(a) (A B )