16. Suppose n balls having weightsw1,w2, . . . ,wn are in an urn. These balls are sequentially removed in the following manner: At each selection, a given ball in the urn is chosen with a probability equal to its weight divided by the sum of the weights of the other balls that are still in the urn. Let I1, I2, . . . , In denote the order in which the balls are removed—thus I1, . . . , In is a random permutation with weights.

(a) Give a method for simulating I1, . . . , In.

(b) Let Xi be independent exponentials with rates wi , i = 1, . . . , n. Explain how Xi can be utilized to simulate I1, . . . , In.