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Let Yı, Y2, ...,Yn be an iid sample from a population distribution described by the pdf...

Let Yı, Y2, ...,Yn be an iid sample from a population distribution described by the pdf fy(y|0) = (@+ 1) yº, o<y<1 for 0> - -

Let Yı, Y2, ...,Yn be an iid sample from a population distribution described by the pdf fy(y|0) = (@+ 1) yº, o<y<1 for 0> - -1. (a) Find the MOM estimator of 0. (b) Find the maximum likelihood estimator (MLE) of 0. (c) Find the MLE of the population mean E(Y) = 0 +1 0 + 2 You do not need to prove that the above is true. Just find its MLE.
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Questions pidif, = 10+1 0 +2 012 Of / 0+2 Bry) = (0+1)yº ; ocje, The first population moment about Origui, Mi-Ely) y fry) dy=16 bodig, f(y) = (0+1) yo ocycl likelihood function, L = flyi) (0+1)* ţ Yi n log (0+1) to log Yi i=1 log L a logL + log Yi domeau By Imvasiance Property of M.C.E. is obtained as, +) Ely) the M. L.E. of the populatisia ( Elogy )+1 = 0+2 -1 Elogy +2 :)

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