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 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 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
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Math 303 Assignment 8, out of 25
I. Problems to be handed in:
1. Let cfw_N (t) : t 0 be a Poisson process of rate , and let Sn denote the time of the nth event. Find:
(a) (1 point) E(N (5)
Solution: N (5) is Poisson(5) so its mean is 5. (Math 302 fact: th
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
Solutions to Assignment #2
January 18, 2013
Total marks = [25].
1. 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|C), and the
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]
PCC PCC PCC + PCC PCC PCS + PCC PCS PSC + PC
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 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
Worksheet 7.5 Clicker Question 1
Suppose Y1 , . . . , Yn are IID from some distribution D. What is the null
hypothesis here?
A H0 : D is Expon (), where is known
B H0 : D is Expon (), where is unknown
C H0 : D is Pois (), where is known
D H0 : D is Pois (
Worksheet 7.4 Clicker Question 1
.
The Neyman-Pearson lemma says that here the test should be of the form
Reject H0 : = 0.23 in favour of Ha : = 0.4
if and only if
fY1 ,.,Y10 (y1 , . . . , y10 | = 0.4)
> c.
fY1 ,.,Y10 (y1 , . . . , y10 | = 0.23)
Simplify
Math 303
Solutions to Assignment #8
March 17, 2017
Total marks = [25].
1. Given that N (t) = n, the arrival times are independent and uniform on [0, t]. The probability that an arrival time lies in [0, u] is thus u/t; call this event a success. Then N (u)
March 3, 2017
Math 303 Assignment 7: Due Friday, March 10 at start of class
I. Problems to be handed in:
1. Let cfw_N (t) : t 0 be a Poisson process of rate , and let Sn denote the time of the nth event.
Find:
(a) E(N (5)
(b) E(S3 )
(c) P (N (5) < 3)
(d)
Math 303
Solutions to Assignment #6
March 3, 2017.
Total marks = [25].
1. Suppose that , 0 are distinct SAWs with P,0 > 0. There could be several ways to get
from to 0 . Specifically, suppose that there are m possible pairs (i(j) , g (j) ), j = 1, . . . m