Use Theorem 8 11 to show that, for random samples of size n from a normal population with the variance 2, the sampling distribution of S2 has the mean 2 and the variance 24 n1 (A general formula for the variance of S2 for random samples from any population with finite second and fourth moments may ...

Use Theorem 8.11 to show that, for random samples of size n from a normal population with

Question:

Use Theorem 8.11 to show that, for random samples of size n from a normal population with the variance σ2, the sampling of S2 has the mean σ2 and the variance 2σ4/n–1. (A general formula for the variance of S2 for random samples from any population with finite second and fourth moments may be found in the book by H. Cramer listed among the references at the end of this chapter.)
Theorem 8.11
If and S2 are the mean and the variance of a random sample of size n from a normal population with the mean µ and the standard deviation s, then
1. and S2 are independent;
2. The random variable (n–1)S2/σ2 has a chi-square with n – 1 degrees of freedom.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...