MTHE/STAT455, STAT855
Fall 2013
Stochastic Processes
Assignment #1, Solutions
Total Marks: 37 for 455 and 45 for 855.
1. From Sheet. (10 marks)
(a) (4 marks) First note that if n is even then Xn must
MTHE/STAT455, STAT855
Fall 2014
Stochastic Processes
Assignment 4
Due Friday, Nov.28
1. Consider a continuous time Markov chain with state space S = cfw_1, 2 and generator
matrix
"
#
G=
,
where >
MTHE/STAT455, STAT855
Fall 2014
Stochastic Processes
Assignment #2
Due Tuesday, Oct.14
Starred questions are for 855 students only.
1. Let cfw_Xn : n 0 be a time-homogeneous Markov chain with state sp
MTHE/STAT455, STAT855 Midterm Solutions
Fall, 2013
1. (15 marks)
(a) (7 marks) Dene M1 , M2 and M3 , where Mi is the expected number of steps to
get to the target vertex starting at a vertex that is i
STAT455/855
Fall 2010
Stochastic Processes
Final Exam, Solutions
1. (15 marks)
(a) (8 marks) Let Sm be the number of steps until the walk rst reaches state m
starting in state 0, and let Si,i+1 be the
STAT455/855
Fall 2007
Applied Stochastic Processes
Final Exam, Solutions
1. (15 marks)
(a) (11 marks) Let q = P (Xi > m). This is the same for all Xi , and is equal to
j1
p(1 p)
q=
m
(1 p)j =
= (1 p)
MTHE/STAT455, STAT855
Fall 2012
Stochastic Processes
Final Exam, Solutions
1. (15 marks)
(a) (10 marks) Condition on the rst pair to bond; each of the n 1 adjacent pairs
is equally likely to bond. Giv
STAT 455/855 Midterm Solutions
Fall, 2010
1. (15 marks)
(a) (4 marks) Each individual in the initial population is the root of a Galton-Watson
branching process starting at a single individual. If the
MTHE/STAT455, STAT855 Midterm Solutions
Fall, 2012
1. (15 marks)
(a) (5 marks) Following the hint let mk denote the expected additional number of
rolls required if the rst roll is k. Let X denote the
MTHE/STAT455, STAT855
Fall 2013
Stochastic Processes
Assignment #2, Solutions
Total Marks: for 455 and for 855.
1. From Sheet. (8 marks)
(a) (4 marks) The example should be such that knowing the infor
MTHE/STAT455, STAT855
Fall 2013
Stochastic Processes
Assignment #3, Solutions
Total Marks: 33 for 455 and 43 for 855.
1. From Sheet. (6 marks)
(a) (3 marks) If we sum gij (n) over n we get the probabi
MTHE/STAT455, STAT855
Fall 2013
Stochastic Processes
Assignment #4, Solutions
Total Marks: 38 for both 455 and 855.
1. From Sheet. (10 marks)
(a) (4 marks) The problem is to compute the probability th
MTHE/STAT455, STAT855
Fall 2013
Stochastic Processes
Final Exam, Solutions
1. (15 marks)
(a) (6 marks) If fr denotes the probability mass function of the family size in the
modied branching process wi
MTHE/STAT455, STAT855
Fall 2013
Stochastic Processes
Assignment #5, Solutions
Total Marks: 20 for both 455 and 855.
1. From Sheet. (10 marks)
(a) (3 marks) The given expression for Gn is clearly corre
MTHE/STAT455, STAT855
Fall 2014
Stochastic Processes
Assignment #1
Due Friday, Sep.26
Starred questions are for 855 students only.
1. Consider the simple random walk, cfw_Xn : n 0, starting at 0 (X0 =