Use the formula for the joint density of Y1 and Yn shown in Exercise 8.52 and the transformation technique of Section 7.4 to find an expression for the joint density of Y1 and the sample range R = Yn – Y1.
Answer to relevant QuestionsUse 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. 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. A random sample of size n = 81 is taken from an infinite population with the mean µ = 128 and the standard deviation σ = 6.3. With what probability can we assert that the value we obtain for X will not fall between 126.6 ...The actual proportion of men who favor a certain tax proposal is 0.40 and the corresponding proportion for women is 0.25; n1 = 500 men and n2 = 400 women are interviewed at random, and their individual responses are looked ...Use a computer program to verify the five entries in Table IV corresponding to 11 degrees of freedom.
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