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

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Let X Denote The Proportion Of Allotted Time That A Randomly Selected Student Spends Working On A Certain Aptitude Test 1 (31.72 KiB) Viewed 9 times

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) where -1 < 8. A random sample of ten students yields data x₁ = 0.99, X₂ = 0.49, x3 = 0.86, x4 = 0.92, X5 = 0.73, x6 = 0.94, x₂ = 0.79, x = 0.79, xg = 0.90, X10 = 0.65. O (a) Use the method of moments to obtain an estimator of 8 1 (1+x) 1 1 + X ³(x-1)- 1 = 1- X { (0+1)x® (0+1)x 0≤x≤1 otherwise 0 -n Eln(X;) ΣIn(X;) -n n Eln(X;) 1 0 (x - 1) Compute the estimate for this data. (Round your answer to two decimal places.) Eln(X;) n 1 - 1 (b) Obtain the maximum likelihood estimator of 0. Eln(x;) - 1 n 2 2 1 Compute the estimate for the given data. (Round your answer to two decimal places.)