This preview shows pages 1–3. Sign up to view the full content.
Name________________________
Stat 427
Midterm 2
Spring, 2006
Rumsey, Goel
Remarks:
•
There are five problems for a total of 100 points.
•
The number of points for each problem is given in the parenthesis.
•
You must show full work for credit.
Problem 1.(30 points)
Let the random variable X denote the length of time (in hours) for
which a book on a 2hour reserve at a library is actually checked out. The density
function of X is as follows:
01
( )
2

12
0.
xx
f
x
otherwise
≤≤
=
Note: The graph of this function is a triangle with vertices at (0,0), (1,1), and
(2,0).
a.
(8 points)
Find the probability that a randomly selected student who checks
out this book will return it within an hour?
b.
(12 points)
Given that a student checks out the book out for more than an
hour, what is the probability that he/she will keep it for at least 1.5 hour?
c.
(5 points)
Find the median length of time that this book will be checked out.
d.
(5 points)
Find the expected value of the random variable
X
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentName________________________
Problem 2.(30 points)
The joint density function of
X
and
Y
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '09
 Statistics

Click to edit the document details