Let X1, X2, , Xn be a random sample of size n from a population with mean and variance 2 (a) Show that X2 is a biased estimator for 2 (b) Find the amount of bias in this estimator (c) What happens to the bias as the sample size n increases ...

a Show that X is a biased estimator of U ...

Let X1, X2, . , Xn be a random sample of size n from a population with

Question:

Let X1, X2, . , Xn be a random sample of size n from a population with mean μ and variance σ2.
(a) Show that X2 is a biased estimator for μ2.
(b) Find the amount of bias in this estimator.
(c) What happens to the bias as the sample size n increases?