We estimate the unknown mean θ of a random variable X (where X has a finite and positive variance) by forming the sample mean Mn=(X1+⋯+Xn)/n of n i.i.d. samples Xi and then forming the estimator
Θˆ=Mn+1n.
Is this estimator unbiased?
unanswered
Is this estimator consistent?
unanswered
Consider now a different estimator, Θˆn=X1 , which ignores all but the first measurement.
Is this estimator unbiased?
unanswered
Is this estimator consistent?