Let X Denote The Proportion Of Allotted Time That A Randomly Selected Student Sp

Please answer the question in the following image:

1. Let X denote the proportion of allotted time that a randomly selected student spendsworking on a certain aptitude test. Suppose that the pdf of X is ((El+1):r:l9 03mg 10 otherwise ’ f($;9) ={ where 9 > —1. A random sample of twelve students yields data 3:1 = .92, 3:2 = .79, x3 =09,374 = $35,335 = 36,335 = .47,£L‘7 = .73,.’L‘3 = 97,339 = 94,3710 = 77, 11311 = .79,3712 =.92. (a) Use the method of moment estimator to obtain an estimator of 6 and computethe estimate for the given data. (b) Obtain the maximum likelihood estimator of 9 and compute the estimate for thegiven data. (C) If X1, . . . ,Xn are from Bernoulli(p), show that the maximum likelihood estimatoris 16 = nil 223:1 Xi, the sample proportion.

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