Let W have an F distribution with parameters r1 and r2. Show that Z = 1/[1 + (r1/r2)W] has a beta distribution.
Answer to relevant QuestionsLet X1 and X2 be independent chi-square random variables with r1 and r2 degrees of freedom, respectively. Let Y1 = (X1/r1)/(X2/r2) and Y2 = X2. (a) Find the joint pdf of Y1 and Y2. (b) Determine the marginal pdf of Y1 and ...Let X1, X2, X3 be a random sample of size n = 3 from the exponential distribution with pdf f(x) = e−x, 0 < x < ∞. Find P(1 < min Xi) = P(1 < X1, 1 < X2, 1 < X3) Let X1 and X2 be a random sample of size n = 2 from a distribution with pdf f(x) = 6x(1 − x), 0 < x < 1. Find the mean and the variance of Y = X1 + X2. Let X1 and X2 be two independent random variables. Let X1 and Y = X1 + X2 be χ2(r1) and χ2(r), respectively, where r1 < r. (a) Find the mgf of X2. (b) What is its distribution? Let X equal the weight of the soap in a “6-pound” box. Assume that the distribution of X is N(6.05, 0.0004). (a) Find P(X < 6.0171). (b) If nine boxes of soap are selected at random from the production line, find the ...
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