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; theta) = { (theta + 1)xtheta 0 ≤ x ≤ 1
{ 0 otherwise

where −1 < theta. A random sample of ten students yields data
x₁= 0.49, x₂= 0.79, x₃= 0.75, x₄= 0.99, x₅= 0.73, x₆= 0.90, x₇= 0.92, x₈= 0.86, x₉= 0.65, x10 = 0.94.

(a)Use the method of moments to obtain an estimator of theta. Compute the estimate for this data. (Round your answer to two decimal places.)
(b)Obtain the maximum likelihood estimator of theta.. Compute the estimate for the given data. (Round your answer to two decimal places.)