Continuous Probability Distributions
P(x
< 290) = .0386(290 - 284.7) = .2046
c.
P
(
x
≥
300)
=
.0386(310.6 - 300) = .4092
d.
P
(290
≤
x
≤
305) = .0386(305 - 290) = .5790
e.
P
(
x
≥
290)
=
.0386(310.6 - 290) = .7952
4.
a.
1.5
1.0
.5
1
2
3
f
(
x
)
x
0
b.
P
(.25
<
x
<
.75)
=
1 (.50)
=
.50
c.
P
(
x
≤
.30)
=
1 (.30)
=
.30
d.
P
(
x
> .60)
=
1 (.40)
=
.40
5.
a.
P
(10,000
≤
x
<
12,000)
=
2000 (1 / 5000)
=
.40
The probability your competitor will bid lower than you, and you get the bid, is .40.
b.
P
(10,000
≤
x
<
14,000)
=
4000 (1 / 5000)
=
.80
c.
A bid of $15,000 gives a probability of 1 of getting the property.
d.
Yes, the bid that maximizes expected profit is $13,000.
The probability of getting the property with a bid of $13,000 is
P
(10,000
≤
x
<
13,000)
=
3000 (1 / 5000)
=
.60.
The probability of not getting the property with a bid of $13,000 is .40.
The profit you will make if you get the property with a bid of $13,000 is $3000
=
$16,000 -
13,000.
So your expected profit with a bid of $13,000 is
EP ($13,000)
=
.6 ($3000) + .4 (0)
=
$1800.
If you bid $15,000 the probability of getting the bid is 1, but the profit if you do get the bid is only
$1000
=
$16,000 - 15,000.
So your expected profit with a bid of $15,000 is
EP ($15,000)
=
1 ($1000) + 0 (0)
=
$1,000.
6 - 3
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