* 16. Suppose n balls having weights wx, w2,..., wn are in an urn. These balls are sequentially removed from an urn 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 IX9I29 ...9In denote the order in which the balls are removed—thus Ix,..., In is a random permutation with weights.

(a) Give a method for simulating Ix .

(b) Let Xt be independent exponentials with rates wi9 /=

Explain how Xt can be utilized to simulate 7\ .