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The statistic 100/Y is called the coefficient of variation. You can calculate it using 100 * sd(y)/mean(y) in R.
The statistic 100/Y is called the coefficient of variation. You can calculate it using
100 * sd(y)/mean(y) in R. For example, if the data are y=c(3,2,5,3,1,3) then the coefficient of variation is 100 * sd(y)/mean(y)=46.9% . If data are produced as iid from the normal distribution whose mean is =50 and whose standard deviation is =15, then the true coefficient of variation is 100(/)=100(15/50)=30%. But the estimator 100/Y is biased because (i) is itself biased, and (ii) the statistic is a nonlinear function of the mean and standard deviation.
A. Use R to estimate E(100/Y) whenn=5 observations Y1, Y2,..., Y5 iid N(50,152) Y1, Y2, ..., Y5 ~iid N(50, 152) are used to calculate and Y . Use the Law of Large Numbers to accomplish this. (You must generate many, many samples of n=5 observations each. Use the "apply" function.)