1
Dr. V.R. Bencivenga
Wednesday Nov. 10, 2010
Economics 329
Fall 2010
MIDTERM EXAM #2
Instructions:
Answer the questions below in a blue exam book.
Show your work to receive credit
.
This is an
open book, open notes exam.
Where applicable, include
(i)
the sample statistic,
(ii)
the sampling distribution
of the sample statistic, and
(iii)
the reason why this sampling distribution is valid, based on the assumptions of
the question.
This information is necessary to receive credit on problems using a sampling distribution of a
sample statistic.
The exam has
ten problems,
totaling 130 points.
The exam is two hours minutes long.
Good
luck!
(20 points)
1.
A small farmer in a developing country grows wheat and cassava.
Market prices of wheat and cassava
fluctuate from year to year, according to the following joint probability distribution:
X = price per bushel of cassava ($)
2
3
4
5
.2
.05
.05
Y = price per
bushel of wheat ($)
6
.05
.3
.05
7
.05
.05
.2
a.
What is the expected price of wheat?
The variance of the price of wheat?
b.
Are the price of cassava and the price of wheat statistically independent?
Explain why or why
not.
c.
Give the probability distribution of the price of wheat conditional on a price of 4 for cassava.
d.
Compute the expected price of wheat conditional on a price of 4 for cassava, and the variance
of the price of wheat conditional on a price of 4 for cassava.
(15 points)
2.
A manufacturing company wants to maintain careful control over the quality of the bolts it uses.
Each
shipment of bolts, which is very large, is subjected to the following procedure.
A random sample of 15 bolts
is taken from the shipment, and each is tested for defects.
If two or more of the bolts in the sample are
found to be defective, the shipment is returned.
a. The manufacturer's supplier of bolts guarantees that no more than ten percent of its bolts are defective.
If a shipment contains ten percent defectives, what is the expected number of defectives in a sample of
15?
b. If a shipment contains ten percent defectives, what is the probability it will be returned?
c.
Perhaps you think too many shipments are returned, now that you have answered the preceding part.
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 Economics

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