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NAME
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ISyE 3770 — Retake of Test 2
Spring 2007
This is a takehome test and should not take more than a couple of hours. Show all
work, write incredibly neatly, and clearly indicate your answers. Turn the test in at the
beginning of class on Tuesday April 24.
1. If
X
is a random variable with c.d.f.
F
(
x
) = 1

e

λx
,
x
≥
0, ﬁnd
E
[
x
3
]. (This may
take a little calculus.)
2. If
X
is a random variable with m.g.f. 0
.
7
e
t
+ 0
.
3, ﬁnd
E
[
X
2
].
3. If
X
is a random variable with m.g.f. 0
.
7
e
t
+ 0
.
3 and
Y
= 2
X
+ 1, ﬁnd the m.g.f.
of
Y
.
4. If
X
,
Y
, and
Z
are i.i.d. with m.g.f. 3
/
(3

t
), what’s the m.g.f. of
X
+
Y
+
Z
?
5. True or False? Suppose that
X
and
Y
have joint p.d.f.
f
(
x,y
) =
cx
2
/
(1 +
x
+
y
),
1
≤
x
≤
2, 1
≤
y
≤
3, where
c
is the appropriate constant. Then
X
and
Y
are
independent.
6. True or False? Suppose that
X
and
Y
have joint p.d.f.
f
(
x,y
) =
cx
2
/
(1+
x
+
y
), 1
≤
x
≤
y
≤
2, where
c
is the appropriate constant. Then
X
and
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 Spring '08
 goldsman

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