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Please solve all parts [ a ,by Page Cid Date Let B 20 be a population parameter, and let Ry , Xy - - Xn be a random sample from a distribution with probability density function f ( x ; B ) = B ( 1 - x ) Ocx zero otherwise a ) is obtain a method of moments estimator for B , B . iil Suppose = 3 , and My = 0.31 , 2 2 20. 77, 2 3 = 0.93. Find a method of moments estimate of B by iJ find the maximum likelihood estimator for B B. . "] Suppose n = 3, and x 20.31 , 12:0. 77 , 2 2= 0.93 Find the method of moments estimate for a B , B . That is find B = arg man L ( B ) = arg max un L(B ) where L ( B ) = 17 f ( x ; , B ) . Y (] Show that W = - In ( 1 - X) follows a gamma distribu kon . What are the parameters x and O for this Gamma distribution 0) Suppose n = 3 and B= 0.8 . Find P ( - E ((1-X: ) 24.5 ) 121