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NEW QUESTION: 1
You evaluate the monthly performance of your portfolio managers against a broad market index. At the end of each year, you add up the number of months in which their performance exceeded that of the market index. If the probability of beating the market index each month, after expenses and sales loads, is
6 5%, what is the mean and variance of the number of months in a year a manager would beat the index?
A. mean = 8.7, variance = 3.73.
B. mean = 8.7, variance = 2.73.
C. mean = 7.8, variance = 2.73.
For this problem, the number of months in a year a manager would beat the index is a binomial random variable with parameters n = 12 and p = 65%. The mean of a binomial distribution is n*p and the variance is n*p*q, where q = 1 - p. Here, we will obtain a mean of 12 * 65% = 7.8, and a variance of 12 * 35% * 65% = 2.73.