Answer to Question #288367 in Statistics and Probability for Elza

Question

A population has mean μ and variance σ2 . The random variables X1, . . . ,X5 are independent and identically distributed samples from the population. We consider the following possible estimators for μ:

T1 = ¯X = 1/5(X1 + X2 + · · · + X5),

T2 = 1/3(X1 + X2 + X3),

T3 =1/8(X1 + X2 + X3 + X4) +1/2X5,

T4 = X1 + X2,

T5 = X1.

(a) Is any of the estimators consistent?