This preview shows pages 1–2. Sign up to view the full content.
Homework 10
Section 7.1, problems 2, 5,
Section 7.2, problems 2,
Section 7.3, problems 8.
Exercise Problems for Final Exam
1. Suppose that random variables
X
and
Y
have joint density function of the form
f
(
x,y
) =
Ce

x
+
y

x

y

.
•
Determine the value of
C
,
•
ﬁnd the marginal density function of
X
and
Y
,
•
ﬁnd
E
(
X
k
)
,V ar
(
X
),
•
ﬁnd
E
(
XY
) and
σ
XY
=
E
(
XY
)

E
(
X
)
E
(
Y
),
•
ﬁnd the conditional density function
f
Y

X
(
y

x
),
•
ﬁnd the conditional expected value
E
(
Y

X
),
2. Let
X
and
Y
be independent uniformly distributed random variables taking values in the interval [0
,
2].
•
Find the density functions of
Z
=
X
+
Y
and
W
=
X

Y
.
•
Are
Z
and
W
independent?
•
What is the covariance
σ
ZW
=
E
(
ZW
)

E
(
Z
)
E
(
W
)? Are they uncorrelated?
3. Let
X
1
,
···
,X
n
,
···
be an i.i.d. sequence of random variables having 1

e

λx
:
x
≥
0 and 0 :
x <
0 as their
common distribution function.
•
What is the distribution function of
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.
 Fall '06
 Caire

Click to edit the document details