72. The logistic pdf f (x)  ex/(1  ex)2 for q 

xqis sometimes used to describe the distribution of measurement errors.

W  X  m ~

a. Graph the pdf. Does the appearance of the graph surprise you?

b. For a random sample of size n, obtain an expression involving the gamma function of the moment generating function of the ith smallest order statistic Yi. This expression can then be differentiated to obtain moments of the order statistics.

Hint: Set up the appropriate integral, and then let u  1/(1  ex).