Let W be a gamma random variable with parameters (t, β), and suppose that conditional on W = w, X1, X2, . . . ,Xn are independent exponential random variables with rate w. Show that the conditional distribution of W given that X1 = x1, X2 = x2, . . . ,Xn = xn is gamma with parameters
Answer to relevant QuestionsA rectangular array of mn numbers arranged in n rows, each consisting of m columns, is said to contain a saddlepoint if there is a number that is both the minimum of its row and the maximum of its column. For instance, in ...Verify Equation (6.6), which gives the joint density of X(i) and X(j). (a) If X has a gamma distribution with parameters (t, λ), what is the distribution of cX, c > 0? (b) Show that has a gamma distribution with parameters n, λ when n is a positive integer and χ22n is a chi-squared random ...Let X have moment generating function M(t), and define ψ(t) = logM(t). Show that ψ′′(t)|t=0 = Var(X) In Example 2h, say that i and j, i ≠ j, form a matched pair if i chooses the hat belonging to j and j chooses the hat belonging to i. Find the expected number of matched pairs.
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