Part A B C 6. Let Y1, Y2. ...,Y be a random sample of n iid continuous random variables drawn from a populationwith the pdf( 2yfy (y) = { 02y > 0elsewhereHere, 0 > 0 is an unknown parameter. You may take as a given (you're welcome!) that the likelihoodfor this sample is2"L(0\y1. 2.... Yn)%3!ej31You may also assume thatE(Y) = V Vo and E(Y*) = 203%3D(a) Find a single statistic which is sufficient for the parameter 0.(b) Determine the method-of-moments estimator of 6, and call it 6.(c) Determine the maximum likelihood estimator of 6, and call it ô.(d) What is the maximum likelihood estimator of vo? Justify your answer by referring to anappropriate result from the notes/textbook.(e) Which of 6, or ô2 is the MVUE of 0? Both? Neither? Make sure to justify your answer.(f) Consider the problem of testing the simple hypotheses Ho: 0 = 1 against H,: 0 = 0a, where0. > 1 is some known constant. Find the form of the rejection region of the most powerfula-level test.(g) Would the uniformly most powerful (UMP) level-a test of Ho: 0 = 1 against H,: 0 >1 havethe same rejection region? Briefly explain why or why not.

Name: Part A B C 6. Let Y1, Y2. ...,Y be a random sample of n iid continuous
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Part A B C 6. Let Y1, Y2. ...,Y be a random sample of n iid continuous random variables drawn from a populationwith the pdf( 2yfy (y) = { 02y > 0elsewhereHere, 0 > 0 is an unknown parameter. You may take as a given (you're welcome!) that the likeliho