4. Let X1, X2, ..., Xn be independent random variables from a distribution with density 1 fo(x) = ő 6.160,00) (2), where

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4 Let X1 X2 Xn Be Independent Random Variables From A Distribution With Density 1 Fo X O 6 160 00 2 Where 1 (88.54 KiB) Viewed 85 times

4. Let X1, X2, ..., Xn be independent random variables from a distribution with density 1 fo(x) = ő 6.160,00) (2), where 0 > 0) is an unknown parameter. Let ôi = X and 62 = nXl:n be estimators of e. = • The bias of ê, is equal to while the bias of ô2 is equal to • The mean square error of ê, is equal to while for ô2 is equal to so for n > 1 the ê, esti- mator is MORE EFFICIENT /LESS EFFICIENT /EQUALLY EF- FICIENT /WE SHOULD NOT TALK ABOUT EFFICIENCY (un- derline the appropriate) than ô2. Hint. If X1, X2, ..., Xn are independent random variables from an expo- nential distribution with parameter 1, then min{X1, X2, ..., Xn} has an exponential distribution with parameter nl.