In Example 8b, let
Show that Y1, . . . ,Yk, Yk+1 are exchangeable. Yk+1 is the number of balls one must observe to obtain a special ball if one considers the balls in their reverse order of withdrawal.
Answer to relevant QuestionsConsider an urn containing n balls numbered 1, . . . , n, and suppose that k of them are randomly withdrawn. Let Xi equal 1 if ball number i is removed and let Xi be 0 otherwise. Show that X1, . . . ,Xn are exchangeable. In Example 5c we computed the conditional density of a success probability for a sequence of trials when the first n + m trials resulted in n successes. Would the conditional density change if we specified which n of these ...Suppose that the number of events occurring in a given time period is a Poisson random variable with parameter λ. If each event is classified as a type i event with probability pi, i = 1, . . . , n, ∑ pi = 1, ...Establish Equation (6.2) by differentiating Equation (6.4). Let X and Y be independent continuous random variables with respective hazard rate functions λX(t) and λY(t), and set W = min(X,Y). (a) Determine the distribution function of W in terms of those of X and Y. (b) Show that ...
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