Quiz 6
Question 1
(1 point)
To find the 98% confidence interval for the population mean, for a
situation in which n is greater than 30, what Z value would you use?
Hint: do not use the Z table or your calculator to find this value. Express your answer to
Quiz10
Question 1
(1 point)
Assume the data below are independent samples from normally distributed populations with the same
variance.
A
B
C
D
19
11
24
14
21
14
19
16
26
21
21
14
24
13
26
13
18
16
20
17
18
13
Use one-way ANOVA to test for a difference in
Quiz 5
Question 1
(1 point)
Use the same data for questions 1, 2, 3, and 4:
The time that it takes to assemble a piece of machinery
is well modeled by the normal distribution with mean of
72.9 minutes and standard deviation of 8.55 minutes.
What is the pr
Quiz 10.
Question 1
(1 point)
The correlation coefficient, r, must have a value between 0 and 1.
Student response: Percent Correct
Student
Answer Choices
Value
Response Response
0.0%
a. true
100.0%
b. false
0.0%
c. not enough information given
General fee
Quiz 1
1) There are eleven quizzes in STAT 263, and all eleven quizzes will count toward the 10% quiz portion of the final
grade. (Hint: It would be useful for this and several other quiz questions to read the course outline and the How
the quizzes work,
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 = 0), where the
probability of moving up at each step is
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 > 0 and > 0.
(a) Show by induction that
"
n
G =
(1)n ( +
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 space S.
(a) Show that, for 1 < r < n and states k and xi
Equations
Tuesday, June 14, 2016
6:04 PM
probability of event A
P(A) = 0.5
P(A B) probability of events
intersection
probability that of events A and
B
P(AB) =
0.5
P(A B) probability of events
probability that of events A or B
P(AB) =
0.5
probability of
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 edges away from the target
vertex. By symmetry, the ex
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 number of steps until the walk rst
reaches state i + 1
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) p
j=m+1
j=0
(1 p)m p
= (1 p)m .
1 (1 p)
(i) (2 marks) T
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. Given that (mr , mr+1 ) is the rst pair to bond the
probab
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 initial population is of
size k then we have k indepen
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 number of rolls required until
two consecutive rolls ar
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 information X0 = 2 in
addition to X1 cfw_3, 4 tells us somet
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 probability that the Y chain ever
visits state j starting in s
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 that there are r arrivals
in the N2 process during an Exp
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 with parameter r then
fr (0) = r + (1 r)f (0)
and
fr (k)
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 correct for n = 1. Assume it is
true for n. Direct matrix mu
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 be even while if n is odd then
Xn must be odd. Also, wh
Student Number
Queens University
Department of Mathematics and Statistics
STAT 353
Midterm Examination February 12, 2009
Total points = 30. Duration = 58 minutes.
This is a closed book exam.
One 8.5 by 11 inch sheet of notes, written on both sides, is
Student Number
Queens University
Department of Mathematics and Statistics
STAT 353
Midterm Examination February 18, 2010
Total points = 30. Duration = 58 minutes.
This is a closed book exam.
One 8.5 by 11 inch sheet of notes, written on both sides, is
STAT 353 Solutions: Assignment 5
Winter, 2014 (Total 30 marks)
Problem 1 (From Sheet.) (9 marks) Expressing Xi and Xj as in the hint, for i = j we have
E[Xi Xj ] = E[(Xi1 + . . . + Xin )(Xj1 + . . . + Xjn )]
n
n
=
E[Xik Xj ]
k=1 =1
n
n
=
P (trial k has ou
Student Number
Queens University
Department of Mathematics and Statistics
STAT 353
Final Examination April 24, 2010
Instructor: G. Takahara
Proctors are unable to respond to queries about the interpretation of exam questions. Do your best to answer exam
Student Number
Queens University
Department of Mathematics and Statistics
STAT 353
Final Examination April 9, 2009
Instructor: G. Takahara
Proctors are unable to respond to queries about the interpretation of exam questions. Do your best to answer exam q
Student Number
Queens University
Department of Mathematics and Statistics
STAT 353
Midterm Examination February 18, 2011
Total points = 30. Duration = 58 minutes.
This is a closed book exam.
One 8.5 by 11 inch sheet of notes, written on both sides, is
Student Number
Queens University
Department of Mathematics and Statistics
STAT 353
Final Examination April 21, 2011
Instructor: G. Takahara
Proctors are unable to respond to queries about the interpretation of exam questions. Do your best to answer exam
STAT 353 Solutions: Assignment 9
Winter, 2014 (Total 30 marks)
Problem 1 (From Sheet.) (5 marks) Let Fn be the distribution function of Xn and let
F (x) = 0 for x < c and F (x) = 1 for x c (i.e., F is the distribution function of a random
variable X that
STAT 353 Solutions: Assignment 3
Winter, 2014 (Total 30 marks)
Problem 1 (From Sheet) (6 marks) The transformation from the variables (X(1) , . . . , X(n) )
to (Y1 , . . . , Yn ) is a one-to-one transformation with inverse
1
Y1
n
1
1
=
Y1 +
Y2
n
n1
1
1
1