In standard confidence intervals, you use the sample mean as an estimator of expected value. Now suppose that a friend of yours suggests the following alternative estimator:

-^"

= Τ7 ρ-^1 "t" TT-^2 + Χ-^3 + ρ-^4 + ' ' ' + ρ-^Ov-1 + η-^ΛΓ \ 2 2 2 2 2 2 where we assume that JV is an even number. Prove that E X 2

= ì, Var (l ) = 1.25 x ^

where E[X] = ì and Var(X) = σ2

. Would you use this estimator? Why or why not?