Use the condition of Exercise 8.9 to show that the central limit theorem holds for the sequence of random variables of Exercise 8.8.
Answer to relevant QuestionsExplain why, when we sample with replacement from a finite population, the results of Theorem 8.1 apply rather than those of Theorem 8.6. Show that, analogous to the formula of Exercise 8.17, the formula for the sample variance can be written as Also, use this formula to calculate the variance of the following sample data on the number of service calls ...Show that if X1, X2, . . . , Xn are independent random variables having the chi-square distribution with v = 1 and Yn = X1 + X2 + · · · + Xn, then the limiting distribution of As n → ∞ is the standard normal ...Use the transformation technique based on Theorem 7.2 on page 218 to rework the proof of Theorem 8.14. Let f = u/v1 v/v2 and w = v.) Verify the results of Example 8.4, that is, the sampling distributions of Y1, Yn, and X~ shown there for random samples from an exponential population.
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