Statistics 252 Winter 2006 Midterm #1 Solutions
1. (a) Since Y1 , Y2 , Y3 are independent and identically distributed we nd
E (Y ) = E
Y1 + Y2 + Y3
3
E (Y1 ) + E (Y2 ) + E (Y3 )
3E (Y1 )
=
= E (Y1 ).
Statistics 252 Midterm #1 January 30, 2006
This exam has 5 problems and 6 numbered pages.
You have 50 minutes to complete this exam. Please read all instructions carefully, and check your
answers. Sho
Statistics 252Mathematical Statistics
Winter 2007 (200710)
Final Exam Solutions
Instructor: Michael Kozdron
1. (a) By denition, the likelihood function L() is given by
n
n
fY (yi |) =
L() =
i=1
n
2
2
Statistics 252 Practice Midterm (Solutions) Winter 2007
1.
Let U = Y / so that for u > 0,
u
2y
y2
exp 2
2
P (U u) = P (Y u) =
0
2
dy = 1 eu .
Thus, we must nd a and b so that
a
2
2ueu du =
0
and
2
2
2
Final Exam Solutions
1. (a) To nd the method of moments estimator, we equate the rst population moment
with the rst sample moment. Since E(Yi ) = 3, we conclude MOM = Y .
3
1. (b) By denition, the lik
Final Exam April 21, 2006
Problem 1. Suppose that Y1 , . . . , Yn are independent and identically distributed random
variables with each Yi having density function
y2
exp cfw_y/ , y > 0,
2 3
where > 0
Statistical Inference
Making decisions regarding the
population base on a sample
Decision Types
Estimation
Deciding on the value of an unknown parameter
Hypothesis Testing
Deciding a statement reg
Using SPSS
Note: The use of another statistical package
such as Minitab is similar to using SPSS
After starting the SSPS program the following dialogue
box appears:
If you select Opening an existing f
Statistics 252 Midterm #2 March 16, 2007
This exam has 5 problems and is worth 40 points.
Instructor: Michael Kozdron
You must answer all of the questions in the exam booklet provided.
You have 50 min
Statistics 252 Winter 2007 Midterm #2 Solutions
1. If Y Uniform(, 2), then fY (y |) = 1 , y 2. Let U = Y / so that if 1 u 2, then
u
P (U u) = P (Y u) =
1
dy = u 1,
2
a
and so fU (u) = 1, 1 u 2. We mus
Statistics 252 Practice Midterm Winter 2007
1.
(8 points ) Consider a random variable Y with density function
fY (y ) =
y2
2y
exp 2
2
,
y > 0,
where > 0 is a parameter. Use the pivotal method to verif
Statistics 252 Winter 2007 Midterm #1 Solutions
1. (a) Since B () = E () , we must rst compute E (). To determine E (), we need to nd
the density function of , which requires us rst to nd the distribu
Make sure that this examination has 11 numbered pages
University of Regina
Department of Mathematics & Statistics
Final Examination
200710
(April 20, 2007)
Statistics 252-001
Mathematical Statistics
N
Statistics 252 Midterm #2 March 3, 2006
1.
(10 points )
(a) Suppose that a random variable Y has density function fY (y |) = ( + 1)y , 0 y 1.
Determine the Fisher information I () for this random vari
CMPT 280
Topic 1: Review of Lists
Mark G. Eramian
University of Saskatchewan
Mark G. Eramian
CMPT 280
1/12
References
Textbook, Chapter 1
Mark G. Eramian
CMPT 280
2/12
Array-based List Implementation
CMPT 280
Intermediate Data Structures and Algorithms
Introduction
Mark G. Eramian
University of Saskatchewan
Mark G. Eramian
CMPT 280
1/17
Course Website
CMPT 280 course on Moodle:
http:/moodle.cs.us
Statistics 252 Midterm #1 February 5, 2007
This exam has 5 problems and is worth 40 points.
Instructor: Michael Kozdron
You must answer all of the questions in the exam booklet provided.
You have 50 m