probability

Bias and MSE

We estimate the unknown mean θ of a random variable X with unit variance by forming the sample mean Mn=(X1+⋯+Xn)/n of n i.i.d. samples Xi and then forming the estimator

Θˆn=13⋅Mn.

Your answers below can be functions of θ and n. Follow standard notation and use 'theta' to indicate θ.

The bias E[Θˆn]−θ of this estimator is:
unanswered

The mean squared error of this estimator is:
unanswered

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