STAT 3502
Assignment # 2
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.
a. the pmf of M is:
b. The cdf of M is:
m
1
2
3
4
5
6
P(m)
1/36
3/36
5/36
7/36
9/36
11/36
F(m)
1/36
4/36
9/36
11/36
25/36
1
2.
[2] Let x = the outcome when a fair die is rolled once. If before the die is rolled
=
=
=
=
=
=
=
6
m
11/36
5
m
9/36
4
m
7/36
3
m
5/36
2
m
3/36
1
m
1/36
)
(
m
P
=
=
=
=
=
=
=
≤
=
6
m
1
5
m
25/36
4
m
11/36
3
m
9/36
2
m
4/36
1
m
1/36
)
(
)
(
m
M
P
m
F
0
1
2
3
4
5
6
7
1
2
3
4
5
6
m=number of t ow t osses
F(m)
)
1
(
)
(
1
X
E
X
E
=
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View Full Documentyou 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
3. The weekly demand for propane gas (in 1000s of gallons) from a particular
facility is a r.v. x with pdf
a. [1.5] Compute the cdf of x.
b. [1.5] What is the value of (median)?
c. [1.5] Compute E(X) and V (X).
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 Summer '09
 JHONBRAN
 Cumulative distribution function, Dice, Yorkshire Television, thousands gallons

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