Looking 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.
Answer to relevant QuestionsHow many different samples of size n = 3 can be drawn from a finite population of size (a) N = 12; (b) N = 20; (c) N = 50? A random sample of size n = 100 is taken from an infinite population with the mean µ = 75 and the variance σ2 = 256. (a) Based on Chebyshev’s theorem, with what probability can we assert that the value we obtain for X ...Independent random samples of sizes n1 = 30 and n2 = 50 are taken from two normal populations having the means µ1 = 78 and µ2 = 75 and the variances σ21 = 150 and σ22 = 200. Use the results of Exercise 8.3 to find the ...A random sample of size n = 12 from a normal population has the mean x = 27.8 and the variance σ2 = 3.24. If we base our decision on the statistic of Theorem 8.13, can we say that the given information supports the claim ...Use the result of Exercise 8.56 to find the probability that the range of a random sample of size n = 5 from the given uniform population will be at least 0.75.
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