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STAT 3502
Assignment # 2
Total mark=25
Due: 21 June, 2010 prior to the start of class
1. Two fair sixsided dice are tossed independently. Let
M
= maximum of the two tosses.
a.
[2] What is the pmf of
M
?
b.
[2] Determine the cdf of
M
and graph it.
2. [2] Let
x
= the outcome when a fair die is rolled once. If before the die is rolled you
are oﬀered either
1
3
.
5
dollars or
h
(
x
) =
1
x
dollars , would you accept the guaranteed
amount or would you gamble? Note: It is not generally true that
1
E
(
X
)
=
E
(
1
X
)
3. The weekly demand for propane gas (in 1000s of gallons) from a particular facility is
a r.v.
x
with pdf
f
(
x
) =
(
2(1

1
x
2
)
1
≤
x
≤
2
0
o.w.
a.
[1.5] Compute the cdf of
x
.
b.
[1.5] What is the value of ˜
μ
(median)?
c.
[1.5] Compute
E
(
X
) and
V
(
X
).
d.
[1.5] If 1.5 thousands gallons are in stock at the beginning of the week and no new
supply is due in during the week, how much of the 1.5 thousands gallons is expected
to be left at the end of the week. (Hint: Let
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 Spring '09
 JHONBRAN

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