Answer to Question #286754 in Statistics and Probability for Rahul

Statistics and Probability

Question #286754

Let x be Bin(n,p). Find the mean square error of the p parameter estimator

Expert's answer

"MSE(\\hat p)=E[(\\hat p-p)^2]=E[(X\/n-p)^2]=E[X^2\/n^2-2pX\/n+p^2]="

"=E[X^2]\/n^2-2pE[X]\/n+p^2=np((n-1)p+1)\/n^2-2np^2\/n+p^2="

"=p(1-p)\/n"

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