Use the result of Exercise 8.58 to show that, for the random variable P defined there,
What can we conclude from this about the distribution of P when n is large?
Answer to relevant QuestionsLooking at binomial random variables as on page 226, that is, as sums of identically distributed independent Bernoulli random variables, and using the central limit theorem, prove Theorem 6.8 on page 191. Find the value of the finite population correction factor N – n / N – 1 for (a) n = 5 and N = 200; (b) n = 50 and N = 300; (c) n = 200 and N = 800. Independent random samples of sizes 400 are taken from each of two populations having equal means and the standard deviations σ1 = 20 and σ2 = 30. Using Chebyshev’s theorem and the result of Exercise 8.2, what can we ...A random sample of size n = 25 from a normal population has the mean x = 47 and the standard deviation σ = 7. If we base our decision on the statistic of Theorem 8.13, can we say that the given information sup–ports the ...The following is a sufficient condition, the Laplace-Liapounoff condition, for the central limit theorem: If X1, X2, X3, . . . is a sequence of independent random variables, each having an absolute third moment And if Where ...
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