NEW YORK UNIVERSITY
DEPARTMENT OF ECONOMICS
Statistics ECONUB.18.011: Fall 2011
Professor Roman Frydman
Solutions to TEST#1
Please answer all questions.
Total 25 points.
Problem 1
.
(4 points)
Consider the following sample
{
1, 2, 3, 4, 5
}
.
A)
What number should be added or subtracted to each one of numbers
in the sample, so the resulting sample has a mean zero? Compute
and brie±y explain.
Answer: Sample average should be subtracted: Here, the sample
average of the 5 numbers is 3.
B)
By what number should you divide each number in the sample, so
the resulting sample has a variance of 1?
Answer: Each number should be divided by sample standard de
viation so that te sample has sample standard deviation of 1 (note
that sample standard deviation of 1 implies sample variance of 1).
Here, sample standard deviation is
√
2
.
5.
Problem 2
.
(5 points)
Consider two randomly selected corporate bonds: A and B. Suppose
that the probability that bond A defaults is 0.5. If bond A defaults, the
probability that bond B defaults is 0.75, whereas if bond A does not
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 Fall '11
 RomanFrydman
 Economics, Standard Deviation, Variance, Sample standard deviation, Professor Roman Frydman

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