Econ 506, Section M1
NAME:_
SOLUTION_
_____
Quiz 2B, Sept. 30, 2010
Total points: 50
I.
The probability that you find a defective machine in a warehouse is 0.2. A company
selects the machines randomly.
a. (4 points)
the company repairs the defective ones at a cost of $50 each. Find the mean
and variance of the total repair cost, if the company selects 5 machines.
let
Y
= # of defective machine selected in 5 machines
E
(50
Y
) = 50
E
(
Y
) = 50[5
(
29
10
2
] = $50.
Furthermore,
V
(50
Y
) = 2500
V
(
Y
) = 2500[5
(
29
10
8
10
2
]
= 2000.
b. (5 points)
what is the probability that the third defective machine is found on the
selection of the fifth machine?
let
Y
= # of machine selected until third defective is found.
Therefore,
Y
is negative
binomial where
r
= 3 and
p
= 0.4.
Then,
P
(
Y
= 5) =
(
29
(
29
083
.
6
.
0
4
.
0
2
4
3
3
=
.
II.
Let Y be a continuous random variable, with the following probability density
function:
≤
≤
≤
≤
=
elsewhere
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 Fall '08
 Staff
 Normal Distribution, Probability theory, probability density function, Cumulative distribution function, Minimum Wage Workers

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