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Unformatted text preview: T ) = p (1p ). (c) Show that P ( T = 1  W = w ) = w ( nw ) n ( n1) . (d) Show that E( T  W ) = n n1 W n 1W n = n n1 Y (1Y ) and, explain why n Y (1Y ) ( n1) is a UMVUE of p (1p ). (iv) Let Y 1 ,...,Y n be an i.i.d. sample from the pdf: f ( y  ) = ( 3 y 2 3 , if 0 y , otherwise where 0 < < . (a) Check whether the pdfs form an exponential family. (b) Show that Y ( n ) = max { Y 1 ,...,Y n } is a sucient statistic. (c) Show that Y ( n ) has pdf: f Y ( n ) ( y  ) = ( 3 ny 3 n1 3 n , if 0 y , otherwise (d) Show that Y ( n ) is complete by denition. (e) Find a UMVUE of ....
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 Spring '11
 lisa

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