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STAT 225  Homework 6
Due Friday June 12
Comments:
1. This homework is due Friday, June 12 in class,
BEFORE
class starts.
2. Please remember
staple
if you turn in more than one page.
3. You must always SHOW ALL WORK. If you do not show your work, you may not receive
full credit.
Do the following problems.
1. Show that if
X
∼
U
(
a, b
) then
V
(
X
) =
(
b

a
)
2
12
.
Guidance:
•
You can use the fact (which we proved in class) that
E
(
X
) =
a
+
b
2
•
It would be useful to know that
a
3

b
3
= (
a

b
)(
a
2
+
ab
+
b
2
))
2. Page 177, problems 4.48
3. Page 176, problem 4.43
4. Page 183, problem 4.64
(a)
5. Page 183, problem 4.65
6. Let
X
∼
N
(0
,
1). Find
E
(
e
3
X
+
e

X
2
/
2
)
Comment:
It would be useful to go over the last example about the normal distribution
that I presented in class in lecture 14 (6/8).
Also, remember that
E
[
g
1
(
X
) +
g
2
(
X
)] =
E
[
g
1
(
X
)] +
E
[
g
2
(
X
)]
7. Page 190, problem 4.91 +
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 Summer '09
 TOM

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