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
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
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
STAT 353 Solutions: Assignment 4
Winter, 2014 (Total 33 marks)
Problem 1 (From Sheet.) (5 marks) We have seen in class that (1/2) = . This
handles the n = 0 case. For n 1, using the recursive property of the Gamma function,
() = ( 1)( 1) for > 1, we have
STAT 353 Solutions: Assignment 1
Winter, 2014 (Total 30 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 the possible values of (X, Y, Z) are those in the set
S(X,Y,
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
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 2
Winter, 2014 (Total 25 marks)
Problem 1 (From Sheet.) (5 marks) First, we note that S S1 . . . Sn . For it not, there
must be some point (x1 , . . . , xn ) S such that xi Si for some i. But since for such an i,
/
P (Xi = x
STAT 353 Solutions: Assignment 6
Winter, 2014 (Total 35 marks)
Problem 1 (From Sheet.) (5 marks) The covariance between X1 and X2 with respect to
the conditional joint distribution of X1 and X2 given Y = y is
[Cov(X1 , X2 ) Y = y] = E[X1 X2 Y = y] E[X1 Y
STAT 353 Solutions: Assignment 8
Winter, 2014 (Total 25 marks)
Problem 1 (From Sheet.) (8 marks) Markovs inequality gives
P (X k)
E[X]
= .
k
k
To apply Chebyshevs inequality we rst need to subtract and take absolute values:
P (X k) = P (X k ) P (|X | k )