Stat 352 Winter 2008
Assignment #3
This assignment is due at the beginning of class on Thursday, February 7, 2008.
1.
Donated blood is screened for AIDS. Suppose that the test has 99% accuracy, and that one
in ten thousand people in your age group are HIV
University of Regina
Department of Mathematics & Statistics
Final Examination (PART I)
200810
Statistics 352
Advanced Mathematical Statistics
Instructor: Michael Kozdron
This nal exam consists of two parts.
Part I of this exam is due at 9:00 am on Tuesday
Stat 352 Winter 2008
Assignment #4
This assignment is due at the beginning of class on Thursday, February 28, 2008.
1.
Construct an equaltailed 90% Bayesian credible interval for using the posterior distribution
given in Problem #2(b) on Midterm #1.
2.
C
Stat 352 Winter 2008
Assignment #2
This assignment is due at the beginning of class on Thursday, January 31, 2008.
1.
Suppose that for each individual of a large population there is a pair of genes, each of which
can be either x or X, that controls eye co
Statistics 352Advanced Mathematical Statistics
Winter 2008 (200810)
Final Exam Solutions
Instructor: Michael Kozdron
1. (a) The likelihood function is
4
f (y ) =
i=1
1
1
f (yi ) = 2 2 exp
4
2
4
(yi 1)2
i=1
and so the posterior density satises
f (y )
Stat 352 Winter 2008
Assignment #1
This assignment is due at the beginning of class on Tuesday, January 22, 2008.
1.
Compute the approximate value of
1
x2 dx
0
using a Riemann midpoint sum and four partitions of equal width.
2.
Approximately 1/125 of all
Stat 352 Winter 2008
Assignment #5
This assignment is due at the beginning of class on Thursday, March 20, 2008, except for Problems 1.(a)
and 1.(b) which are due at the beginning of class on Tuesday, March 18, 2008.
1.
Suppose that the random variable Y
Stat 352: Solutions to Assignment #1
1. Using a Riemann midpoint sum with four partitions of equal width gives
1
x2 dx
0
1
4
1
8
2
+
2
3
8
5
8
+
2
+
7
8
2
=
21
= 0.328125.
64
2. Note that a special case of Bayes Theorem follows from the denition of condi
Statistics 352 Midterm #1 February 12, 2008
This exam is worth 60 points.
This exam has 8 problems and 8 numbered pages.
You have 75 minutes to complete this exam. Please read all instructions carefully, and check
your answers. Show all work neatly and in
Statistics 352 Midterm #2 April 3, 2008
This exam is worth 32 points.
This exam has 3 problems and 2 numbered pages.
You have 75 minutes to complete this exam. Please read all instructions carefully, and check
your answers. Show all work neatly and in ord
Statistics 352 Winter 2008 Midterm # 2 Solutions
1. (a) The posterior density is given by
f (y = 1) = C
4 e/2
e 1
where C satises
4 /2
1
e
=
d.
C
e 1
0
Using Maple we can nd the value of C as follows.
> Int(x^4*exp(x/2)/(exp(x)1),x=0.infinity);
> eval
Statistics 352 Winter 2008 Midterm # 1 Solutions
1. (a) Using Bayes rule we nd
P cfw_Box i  black ball =
P cfw_black ball  Box iP cfw_Box i
P cfw_black ball
where
3
P cfw_black ball =
P cfw_black ball  Box iP cfw_Box i =
i=1
11 11 11
13
+=.
23 33 43
36
Stat 352: Solutions to Assignment #3
1. By Bayes theorem, we have
P (you have AIDStest positive) =
P (test positiveyou have AIDS) P (you have AIDS)
.
P (test positive)
We now use the information given in the problem, but need to be careful about the wor
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