SPRING 2009
MATH 425
Ralf Spatzier
Homework 5
for Wednesday, June 10
(1) The random variables
X
and
Y
have the joint density function
f
(
x,y
) = 12
x y
(1

x
) for )
< x <
1
,
0
< y <
1
and equal to 0 otherwise.
(a) Are
X
and
Y
independent?
(b) Find
E
[
X
].
(c) Find
E
[
Y
].
(d) Find
V ar
(
X
).
(e) Find
V ar
(
X
).
(2) Three points
X
1
,X
2
,X
3
are selected a t random on a line
L
of length 1. What is the
probability that
X
2
lies between
X
1
and
X
3
?
(3) Let
X
and
Y
have joint density function
f
(
x,y
) =
1
x
2
y
2
x
≥
1
,y
≥
1
.
(a) Compute the joint density function of
U
=
XY
and
V
=
X/Y
.
(b) What are the marginal densities of
U
and
V
?
(4) The gross daily sales at Amer’s is a normal random variable with mean $2
,
200 and
standard deviation $230. What is the probability that
(a) that the total gross sales over the next 2 days exceed $5,000?
(b) That the daily sales exceed $2,000 in at least 2 of the next 3 days?
(5) Suppose
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '10
 k
 Math, Probability theory, joint density function, Ralf Spatzier, radie 1,2

Click to edit the document details