Answered: ) Annual returns on the more than 5000 common stocks available to investors vary a lot. In a recent year, the mean return was 8.3% and the standard deviation of…

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Question

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(a) Annual returns on the more than 5000 common stocks available to investors vary a lot. In a recent year, the mean return was 8.3% and the standard deviation of return was 28.5%. The law of large numbers says that

A. you can get an average return higher than the mean 8.3% by investing in a large number of stocks.
B. as you invest in more and more stocks chosen at random that year, your average return on these stocks gets ever closer to 8.3%.
C. if you invest in a large number of stocks chosen at random, your average return will have approximately a Normal distribution.
D. None of the above.

(b) The number of hours a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The central limit theorem says that

A. as we look at more and more bulbs, their average burnout time gets ever closer to the mean for all bulbs of this type.
B. the average burnout time of a large number of bulbs has a distribution that is close to Normal.
C. the average burnout time of a large number of bulbs has a distribution of the same shape (strongly skewed) as the distribution for individual bulbs.
D. None of the above.

(c) The Bureau of Labor Statistics announces that last month it interviewed all members of the labor force in a sample of 60000 households; 4.9% of the people interviewed were unemployed. The boldface number is a

A. statistic.
B. parameter.
C. sampling distribution.
D. None of the above.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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