Homework 3 Solutions
Note: Solutions are incomplete if the solution to the first part is a good representation of the solutions
to the other parts.
3.75
a.
(
29
(
29
(
29
(
)
(
)
(

)
(
)

.3(.4)
.8(.6)
.12
.48
.6
P A
P A
B
P A
B
P A B P B
P A B P B
=
+
=
+
=
+
=
+
=
I
I
b.
(
)
(

)
(
)
.3(.4)
(

)
.2
(
)
(
)
.6
P B
A
P A B P B
P B
A
P A
P A
=
=
=
=
I
c.
(
29
(
29
(
29
.7(.4)
.28

.7
.7(.4)
.2(.6)
.4
P B
A
P B
A
P A
=
=
=
=
+
I
3.78
V and W consider bidding.
V will definitely put in a bid, and
3
4
(

)
P Vgets Wnotbid
=
3
4
1
3
(
)
(

)
P Wbid
P Vgets Wbid
=
=
a.
P(V gets job) = ¾*1/3+1/4*3/4=.4375
b.
P(W did not bid  V gets job) = P(W did not bid and V gets job) / P(V gets job)
=1/4*3/4 / .437=.4286
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4.3
a. All values ≥0 and add to exactly 1, so this is a probability distribution.
b. The values add to >1, so this can’t be a probability distribution.
c. Not all values ≥0, so this is not a probability distribution.
4.4
a. not add to 1;
b. For x=2, the probability will be negative, so this is not a probability distribution;
c. All values ≥0 and they add to 1, so this is a probability distribution.
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 Spring '08
 Mendell
 Probability distribution

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