Math 340
Spring 2013
Mock midterm
3/19/13
Time Limit: 60 Minutes
Name (Print):
Student number
This exam contains 4 pages (including this cover page) and 2 problems. Check to see if any
pages are missing. Enter all requested information on the top of this
MATH 302
Sample midterm 2
1. A random variable X has cumulative distribution function
if x < 0
0
x
1
if 0 x < 4
2
FX (x) = 3
2 x if 1 x < 1
4
2
1
if x 1 .
2
(a) Find P (X = 1 ).
2
(b) Find P (X < 1 ).
4
(c) Find P (X 2 ).
3
(d) Find a so that P(X a) = 1
MATH 340 Homework 1
Due January 17 (in class)
Some HW questions are from the Chvatals book. (Linear programming
by Vaek Chvtal.) If you dont have a copy of the book yet, then there is
s
a
one temporarily shelved at I.K. BARBER LEARNING CENTRE circulation
Be sure this exam has 9 pages including the cover
The University of British Columbia
Sessional Exams 2011 Term 2
Mathematics 303 Introduction to Stochastic Processes
Dr. D. Brydges
Last Name:
First Name:
Student Number:
This exam consists of 8 questions w
Be sure this exam has 12 pages including the cover
The University of British Columbia
Sessional Exams 2013 Term 2
Mathematics 303 Introduction to Stochastic Processes
Dr. G. Slade
Last Name:
First Name:
Student Number:
This exam consists of 8 questions wo
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Math 303 Assignment 2
I. Problems to be handed in:
1. (5 points) Ross 4 #58.
Solution: Following the hint, we compute
P (Xn+1 = i + 1|Xn = i, lim Xm = N ) =
m
P (Xn+1 = i + 1, limm Xm = N |Xn = i)
.
P (limm Xm = N |Xn = i)
Using P (A B|C) = P (A|B C)P (B|
Math 303 Assignment 1
I. Problems to be handed in:
1. (6 points) Ross 4 #5 A Markov chain (Xn,n0 ) with states 0, 1, 2 has the transition probability matrix
3 2 1
1
P = 0 2 4 .
6
3 0 3
If P (X0 = 0) = P (X0 = 1) = 1/4 find E[X3 ].
Solution: The transition
Math 303 Assignment 3
I. Problems to be handed in:
1. For simple random walk on Z with probability of stepping to the right p 6= 12 , show that state 0 is
transient. Suggestion: as a function of p, r = 4p(1 p) is an upside down parabola whose maximum
occu
Math 303 Assignment 2, out of 25
I. Problems to be handed in:
1. (5 points) Ross 4 #58. In the gamblers ruin problem of Section 4.5.1, suppose that the gamblers fortune
is presently i and that we know that the gambler will eventually break the bank, that
Be sure this exam has 12 pages including the cover
The University of British Columbia
Sessional Exams 2011 Term 2
Mathematics 303 Introduction to Stochastic Processes
Dr. D. Brydges
Last Name:
First Name:
Student Number:
This exam consists of 8 questions
Math 303 Assignment 5, out of 25
I. Problems to be handed in:
1. This question continues the problem on the previous homework, which you should review, because parts
of this problem use the previous one. You should also review our notes to see how indicat
Math 303 Midterm Test, February 2014
Closed book exam, no calculators.
Explanation is required whenever it is not clear how answers are obtained.
The test has 4 questions and is out of 40.
First Name:
Last Name:
Student Number:
Question Points Score
1
10
Math 303 Midterm Test 2, March 2014
Closed book exam, no calculators.
Brief explanation is required whenever it is not clear how answers are obtained.
The test has 4 questions and is out of 40.
First Name:
Last Name:
Student Number:
Question Points Score
J.J. (Jun Jie) Qian
Re: Application to UBC Stern PhD Finance program
Since childhood, I have been fascinated by stories behind stock market movement. At university, my multiple
research / teaching assistant experience sparked my interests in a career in a
Math 303
Solutions to Assignment #1
January 11, 2011
Total marks = [25].
1. (a) By taking into account each of the 8 possibilities for Garys non-glum state on the
following three days, we obtain the result:
[4]
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Math 303 Assignment 4
Reminder: Test 1 will be held in class on Friday February 10, and will be based on the material covered in
Assignments 14. No assignment will be given on February 3; Assignment 5 will be available on February
10.
I. Problems to be ha
Math 303 Assignment 5, out of 25
I. Problems to be handed in:
1. The goal of this question is to show that symmetric simple random walk on Z3 is transient. It may
return to the origin a few times, but eventually wanders away to explore its universe and ne