# Question: Verify the identity Which we used in the proof of

Verify the identity

Which we used in the proof of Theorem 8.11.

Which we used in the proof of Theorem 8.11.

## Answer to relevant Questions

Use Theorem 8.11 to show that, for random samples of size n from a normal population with the variance σ2, the sampling distribution of S2 has the mean σ2 and the variance 2σ4/n–1. (A general formula for the variance of ...Use the results of Exercises 8.25 and 8.27 to show that if X has a chi-square distribution with v degrees of freedom, then for large v the distribution of √2X – √2v can be approximated with the standard normal ...If X1, X2, . . . , Xn are independent random variables having identical Bernoulli distributions with the parameter θ, then is the proportion of successes in n trials, which we denote by Θ. Verify that (a) E(Θ) = θ; ...Find the sampling distribution of the median for random samples of size 2m+ 1 from the population of Exercise 8.46. Use the result of Exercise 8.54 and that of part (a) of Exercise 8.52 to find the sampling distribution of R for random samples of size n from an exponential population.Post your question