MTHE/STAT 353 Winter 2014
Homework Assignment 6
Assignment 6 due Monday, March 10
1. Let X1 and X2 be random variables and Y a random vector. Show the following
generalization of the conditional varia
Student Number
Queens University
Department of Mathematics and Statistics
STAT/MTHE 353
Final Examination April 21, 2012
Instructor: T. Linder
PLEASE NOTE: Proctors are unable to respond to queries a
MTHE/STAT 353 Winter 2014
Homework Assignment 9
Assignment 9 due Thursday, April 3
1. Let X1 , X2 , . . . be a sequence of random variables and let c be a constant. Show that
if, as n , Xn c in distri
MTHE/STAT 353 Winter 2014
Homework Assignment 3
Assignment 3 due Monday, Feb. 3
1. Let X1 , . . . , Xn be independent exponential random variables with parameter , and
let X(1) , . . . , X(n) be their
MTHE/STAT 353 Winter 2014
Homework Assignment 5
Assignment 5 due Monday, March 3
1. Let (X1 , . . . , Xk ) have a multinomial distribution with parameters n and p1 , . . . , pk .
For i = 1, . . . , k,
MTHE/STAT 353 Winter 2014
Homework Assignment 2
Assignment 2 due Monday, Jan. 27
1. A product set in Rn is a set S of the form S = S1 S2 . . . Sn , where Si R for
i = 1, . . . , n, and the set S1 . .
MTHE/STAT 353 Winter 2014
Homework Assignment 1
Assignment 1 due Thursday, Jan. 16
1. An urn contains 12 balls: 3 red balls, 3 blue balls, 3 green balls, and 3 magenta balls.
Nine of the balls are sel
MTHE/STAT 353 Solutions: Assignment 9
Winter, 2017
1. [Section 11.3, #7.]
Let X denote the waiting period from the time the book is ordered until it is received, in
days. Then E[X] = 7 and Var(X) = 4.
MTHE/STAT 353 Solutions: Assignment 2
Winter, 2017
1. [Ghahramani, 9.1, #20]
Since min(X1 , . . . , Xn ) is a nonnegative random variable, for any x > 0 we
P (Yn > x) = P n min(X1 , . . . , Xn ) > x
x
MTHE/STAT 353 Solutions: Assignment 5
Winter, 2017
1. [Ghahramani, 10.4, #6.]
Let X denote the length of a message (in bits), so that T = X/1000. Let Xi , i 1, be the
number of bits in the ith charact
MTHE/STAT 353 Solutions: Assignment 7
Winter, 2017
1. [Ghahramani, 11.1, #9.]
If X has a geometric distribution with parameter p, then its moment generating function is
calculated as follows.
tX
MX (t
MTHE/STAT 353 Solutions: Assignment 1
Winter, 2017
1. [An urn contains 12 balls . . . ]
(a) After 9 draws, the total number of red, blue and green balls must be at least 6, so the possible
values of (
MTHE/STAT 353 Solutions: Assignment 2
Winter, 2016 (Total 30 marks)
Problem 1 (From Sheet.) (5 marks) First, the marginal distribution of each Xi is given by
P (Xi = 1) = P (both endpoints of edge i h
STAT 353 Solutions: Assignment 5
Winter, 2016 (Total 25 marks)
Problem 1 (From Sheet.) (4 marks)
(a) (2 marks) We can define three random variables, say Y1 , Y2 and Y3 , where Y1 is the
number of Xs t
STAT 353 Solutions: Assignment 6
Winter, 2016 (Total 25 marks)
Problem 1 (From Sheet.) (4 marks) On problem 5 of homework 4 it was computed that
E[Xi Xj ] = n(n 1)pi pj . Therefore, to compute Cov(Xi
STAT 353 Solutions: Assignment 3
Winter, 2016 (Total 27 marks)
Problem 1 (From Sheet.) (6 marks)
(a) (3 marks) From the binomial theorem
k
k )
1
1
1
1
1
1
+
+ 1
2
n
n
n
n
( k
km m X
km
m )
k
1 X
STAT 353 Solutions: Assignment 8
Winter, 2016 (Total 32 marks)
Problem 1 (From Sheet.) (4 marks) Let MX (t) denote the moment generating function of
X. Following the hint, writing MX (t) in a Taylor s
MTHE/STAT 353 Solutions: Assignment 1
Winter, 2016 (Total 26 marks)
Problem 1 (From Sheet.) (6 marks)
(a) (3 marks) After 9 draws, the total number of red, blue and green balls must be at least
6, so
STAT 353 Solutions: Assignment 4
Winter, 2016 (Total 28 marks)
Problem 1 (From Sheet.) (5 marks) For a given n, the probability we want to compute is
P (X(1) < 1/2, X(n) > 1/2). The joint pdf of (X(1)
STAT 353 Solutions: Assignment 7
Winter, 2016 (Total 30 marks)
Problem 1 (From Sheet.) (6 marks)
(a) (3 marks) Let X denote the number of flips required until at least one head and one
tail have been
MTHE/STAT 353 Solutions: Assignment 8
Winter, 2017
1. [Let X and Y be. . . ]
(a) Let fX and fY denote the marginal pdfs of X and Y , respectively. For x > 0 the
marginal pdf of X at x is computed as
Z
MTHE/STAT 353 Solutions: Assignment 6
Winter, 2017
1. [Ghahramani, 10.2, #4.]
Let X1 be the number of sheep stolen, X2 the number of goats stolen, and X3 the number
of burros stolen. We wish to find C
STAT 353 Solutions: Assignment 3
Winter, 2017
1. [Show that the Gamma(r, ). . . ]
Differentiating f (x) with respect to x, we have
f 0 (x) =
r r2 x
r
(r 1)xr2 ex xr1 ex =
x e
r 1 x .
(r)
(r)
The ter
MTHE/STAT 353 Solutions: Assignment 4
Winter, 2017
1. [Ghahramani, 10.1, #9.]
Fix k < n. The students who belong in seats 1, . . . , k have been called and are not standing.
Define Xk+1 , . . . , Xn a
Student Number
Queens University
Department of Mathematics and Statistics
MTHE/STAT 353
Midterm Examination February 13, 2014
Total points = 30. Duration = 58 minutes.
This is a closed book exam.
O
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 interpr
Student Number
Queens University
Department of Mathematics and Statistics
MTHE/STAT 353
Final Examination April 13, 2013
Instructor: G. Takahara
Proctors are unable to respond to queries about the in
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 interpre
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 interpr