Homework 3Due February 16, 2011
Instruction: Complete all of the problems to receive the full credit. The
total is 30 points.
# 1. Consider a Markov chain cfw_Xn , n 0 with state space cfw_0, 1 and
transition probability matrix
P=
1/3
3/4
2/3
1/4
.
Assumi
Homework 5Due March 16, 2011
Instruction: Complete all of the problems to receive the full credit. The
total is 30 points.
# 1. Let X1 , X2 , . . . be independent and identically distributed exponential random variables with rate .
(a) Please work out the
Homework 3Due February 16, 2011
Instruction: Complete all of the problems to receive the full credit. The
total is 30 points.
# 1. Consider a Markov chain cfw_Xn , n 0 with state space cfw_0, 1 and
transition probability matrix
P=
1/3
3/4
2/3
1/4
.
Assumi
Homework 7 with solutionsDue April 15, 2011
Instruction: Complete all of the problems to receive the full credit. The
total is 30 points. Again, if you have seen any typos, or errors, please let me
know as soon as possible.
# 1: Suppose X N (0, 2 ), Y N (
Homework 6 with SolutionsDue April 6, 2011
Instruction: Complete all of the problems to receive the full credit. The
total is 30 points. Please watch for typos and errors, and kindly let me know.
# 1: There are N = 30 individuals in a population, some of
1
Homework 5 Due March 16, 2011
Instruction: Complete all of the problems to receive the full credit. The
total is 30 points.
# 1. Let X1 , X2 , . . . be independent and identically distributed exponential random variables with rate .
(a) Please work out
Homework 4Due March 4, 2011 (Friday)
Instruction: Complete all of the problems to receive the full credit. The
total is 30 points.
# 1. From the textbook: Page 354, # 1.
Solution: (a) Recall that the rate parameter of an exponential random
variable is the
Homework 2Due February 4, 2011
Instruction: Complete all of the problems to receive the full credit. The
total is 30 points.
# 1. Two white and two black balls are distributed in two urns in such
a way that each contains two balls. We say that the system
Homework 1Due January 26, 2011
Instruction: Complete all of the problems to receive the full credit. The total
is 30 points.
# 1. Suppose that Y1 and Y2 are independent Poisson distributed random
variables with means 1 and 2 , respectively. Let W = Y1 + Y
Homework 7Due April 15, 2011
Instruction: Complete all of the problems to receive the full credit. The
total is 30 points.
# 1: Suppose X N (0, 2 ), Y N (0, 2 ), and X is independent of
Y , please use the method of moment generating functions to nd out th
Homework 6Due April 6, 2011
Instruction: Complete all of the problems to receive the full credit. The
total is 30 points.
# 1: There are N = 30 individuals in a population, some of whom have
a certain infection that spreads as follows. Contacts between tw
Homework 4Due March 4, 2011 (Friday)
Instruction: Complete all of the problems to receive the full credit. The
total is 30 points.
# 1. From the textbook: Page 354, # 1.
# 2. Let Xi , i = 1, 2, 3, be independent exponential random variables
with rates i ,
Homework 1Due January 26, 2011
Instruction: Complete all of the problems to receive the full credit. The
total is 30 points.
# 1. Suppose that Y1 and Y2 are independent Poisson distributed random
variables with means 1 and 2 , respectively. Let W = Y1 + Y