hw2_sol

hw2_sol - 10-2 ^ 1 E ( 1 ) = [ E (x1 ) + E ( x2 ) + . + E (...

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10-2 ^ 1 1 27 ^ 2 164 1 ( ) [( ) () .. . ( )] 7 1 ( ) [ 2( ) ( 2 E E x E x Ex E E x E x qm = + + += = -+= so both are unbiased estimators 22 2 ^ 1 17 2 22 2 ^ 2 1 64 11 ( ) .. . 7 77 2 1 13 ( ) ( ) ( ) 2222 Va r Va r x Va rx Va r Va r x r x s q s q  = +   - = + += 2 ^^ 2 ( ) 7 MS E Va r bias s qq = += 2 2 3 ( ) 2 MS E Va r bias s so ^ 1 q is the better estimator of m , because its MSE is smaller 10-7 ! xc poissondistribution ce px x - = and 1 1 1 ! ! n i i i x cn x c n n i i i i Lc x x = - - = = == now l n ( )
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