Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test.

Suppose the pdf of X is where 1 . A random sample of ten students yields data x1 .92, x2 .79, x3 .90, x4 .65, x5 .86, x6 .47, x7 .73, x8 .97, x9 .94, x10 .77.

u f(x; u) 5 e

(u 1 1)xu 0 # x # 1 0 otherwise gxi x 2 5 16,500

a. Use the method of moments to obtain an estimator of , and then compute the estimate for this data.

b. Obtain the maximum likelihood estimator of , and then compute the estimate for the given data.