STAT455/855
Fall 2005
Applied Stochastic Processes
Assignment #4, Solutions
Total Marks: 40 for 455 and 50 for 855.
1. From Sheet.
(a) (7 marks) For n = 1, we have
k
G1 (s) =
s P (X1 = k ) =
k=0
k
k
(ps)k =
s qp = q
k=0
k=0
q
.
1 ps
It is easily veried th
STAT455/855
Fall 2003
Applied Stochastic Processes
Assignment #3, Solutions
1. From Sheet.
(a) We dene the 4 states to be
State 0 = You have won the game
State 1 = You have lost the game
State 2 = Your next draw will be from urn 1
State 3 = Your next draw
STAT455/855
Fall 2003
Applied Stochastic Processes
Assignment #2, Solutions
Total Marks: 30 for 455 and 40 for 855.
1. From Sheet. (20 marks)
(a) (8 marks) For each of parts (i) and (ii) we may determine the state space by starting in
state (0, 1) and fol
STAT455/855
Fall 2003
Applied Stochastic Processes
Assignment #2, Markov Chains I
Due Monday, Oct.20
Starred questions are for 855 students only.
1. For each of the Markov chains cfw_Xn in parts(a)-(d), nd the state space S , the transition probability m
STAT455/855
Fall 2003
Applied Stochastic Processes
Assignment #1, Solutions
Total Marks: 40 for 455 and 45 for 855.
1. Ross, Chapter 3 #8. (6 marks)
(a) (1 mark) Since X clearly has a Geometric distribution with parameter p = 1/6, E [X ] =
6.
(b) (2 marks
STAT455/855
Fall 2001
Applied Stochastic Processes
Final Exam, Selected Solutions
1. (15 marks)
(a) (2 marks) E [N1 ] = m since N1 is the number of draws required until ball 1 is drawn for
the rst time, so that N1 has a geometric distribution with paramet
STAT455/855
Fall 1999
Applied Stochastic Processes
Final Exam, Selected Solutions
1. (20 marks)
(a) False. A Poisson process reversed in time would be a nonincreasing process, so could
not be a Poisson process.
(b) True. Not discussed this year.
(c) False
Page 1 of 4 Pages
QUEENS UNIVERSITY
DEPARTMENT OF MATHEMATICS AND STATISTICS
STAT 455/855 FALL 1999
FINAL EXAMINATION
2:00PM, DECEMBER 13, 1999
GLEN TAKAHARA
Instructions: This examination is THREE HOURS in length. No notes or books are
allowed. A calcula
Page 1 of 4 Pages
QUEENS UNIVERSITY
DEPARTMENT OF MATHEMATICS AND STATISTICS
STAT 455/855 FALL 2001
FINAL EXAMINATION
2:00PM, DECEMBER 10, 2001
GLEN TAKAHARA
Instructions:
This examination is THREE HOURS in length. It is closed-book no notes or books
are
STAT455/855
Fall 2003
Applied Stochastic Processes
Assignment #5, Solutions
1. Ross, Chapter 6 #1. The state space of the process (N1 (t), N2 (t) is S = cfw_(n, m) : n
0, m 0. If in state i = (n, m), we leave state i as soon as there is a pairing. Accord
STAT455/855
Fall 2003
Applied Stochastic Processes
Assignment #4, The Poisson Process
Due Friday, Nov.21
Starred questions are for 855 students only.
1. Ross, Chapter 5, #43 (Chapter 5, #41 in 7th edition.) (Condition on whether or not
a new arrival nishe