# Question: Find the mean and the variance of the finite population

Find the mean and the variance of the finite population that consists of the 10 numbers 15, 13, 18, 10, 6, 21, 7, 11, 20, and 9.

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Show that the variance of the finite population {c1, c2, . . . , cN} can be written as Also, use this formula to recalculate the variance of the finite population of Exercise 8.16. Prove Theorem 8.10. Theorem 8.10 If X1 and X2 are independent random variables, X1 has a chi-square distribution with v1 degrees of freedom, and X1 + X2 has a chi-square distribution with v > v1 degrees of freedom, then X2 ...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 ...Verify that if T has a t distribution with v degrees of freedom, then X = T2 has an F distribution with v1 = 1 and v2 = v degrees of freedom. Find the sampling distributions of Y1 and Yn for random samples of size n from a population having the beta distribution with α = 3 and β = 2.Post your question