Let (X1, X2, X3, X4) be a random sample from a population characterized by random
variable X. Let μ= E(X) and o² = Var(X).
(a) A researcher proposes Z = 0.1X, +0.2X2 +0.3X3 +0.4.X, as an estimator of μ. Is this estimator unbiased? (Explain).
(b) Calculate Var(Z) in terms of o2.
(c) Use the properties of covariance to calculate Cov(X + 2X2, X1) in terms of o².