Let y1, Y2, · ·· , Yn be a simple random sample of size n. Assume that sampling is with replacement. Recall that 1 y = - 1 Σ s2 = -> (Yi – - 9)°, Yi п — 1 i=1 i=1 µ: the population mean, o²: the...

Extracted text: Let y1, Y2, · ·· , Yn be a simple random sample of size n. Assume that sampling is with replacement. Recall that 1 y = - 1 Σ s2 = -> (Yi – - 9)°, Yi п — 1 i=1 i=1 µ: the population mean, o²: the population variance, and T: population total. (a) Show that E(s²) = o². That is, s? is unbiased estimator of o². (b) Can you conclude that s is unbiased estimator of o? Explain. (c) Derive unbiased estimator of o?, the variance of j. (d) Derive unbiased estimator of o?, the variance of î.