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 f(x; 0) (0+1) = 0 0x1 otherwise where -1 <0. A random sample of ten students yields data x = .92, x = .79, x = .90, x = .65, x, = .86, x = .47, x=.73, xg .97, x9= .94, x10 = .77.

a. Use the method of moments to obtain an estimator of 0.

and then compute the estimate for this data.

b. Obtain the maximum likelihood estimator of 0, and then compute the estimate for the given data.