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STOR 435
Exam 2
Fall 2009
(1) Check “true” or “false”.
(1.1) If
X
∼
Exponential (
λ
),
Y
∼
Exponential (
μ
), and
P
(
X
≤
1)
< P
(
Y
≤
1), then
λ < μ
.
(1.2) If
X
∼
Geometric (
p
1
),
Y
∼
Geometric (
p
2
), and
P
(
X >
1)
> P
(
Y >
1), then
p
1
> p
2
.
(1.3) If
X
∼
Uniform (

1
,
1),
Y
∼
Uniform (

c,c
), and
V arY
= 2
V arX
, then
c
= 2.
(1.4) If
X
and
Y
are iid with
X
∼
Poisson (1), then 2
X
+
Y
∼
Poisson (3).
(1.5) If
X
and
Y
are iid with
X
∼
Poisson (1), then
V ar
(2
X

Y
) = 5.
(1.6) Let
X
and
Y
denote the total numbers of heads and tails among 5 tosses of a coin (
p
)
with
p <
1
/
2, then
P
(
X >
2)
> P
(
Y >
2).
(1.7) If the indicators
I
A
,
I
B
satisfy
P
(
I
A
> I
B
) = 1
/
2, and
A
,
B
are mutually exclusive,
then
P
(
A
) = 1
/
2.
(1.8) Let
X
and
Y
denote the total numbers of heads and tails among 4 tosses of a fair coin,
then
P
(
X

Y
= 1) = 0.
Note: Show your work in each of the following problems.
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This note was uploaded on 11/17/2011 for the course STOR 435 taught by Professor Staff during the Fall '08 term at UNC.
 Fall '08
 Staff

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