An experiment produces random vector X = [X1 ··· Xk]' with expected value µX = [µ1 ··· µk]' The ith component of X has variance Var[Xi] = σ2i . To estimate µX, we perform n independent trials such that X(i) is the sample of X on trial i, and we form the vector mean
(a) Show M(n) is unbiased by showing E[M(n)] = µX.
(b) Show that the sequence of estimates Mn is consistent by showing that for any constant c > 0,
