20. Consider the following procedure for randomly choosing a subset of size k from the numbers 1, 2 , . . . , ç : Fix ñ and generate the first ç time units of a renewal process whose interarrivai distribution is geometric with mean

\/p—that is P {interarrivai time = k) = p(l - p)k~l, k = 1,2, Suppose events occur at times ix < i2 < ··· < im < n. If m = k stop; i l 9 i m is the desired set. If m > k, then randomly choose (by some method) a subset of size k from i l 9 i m and then stop. If m < k, take i l 9 i m as part of the subset of size k and then select (by some method) a random subset of size k - m from the set {1,2, ...,n] - Explain why this algorithm works. As E[N(n)] = np a reasonable choice of ñ is to take ñ « k/n. (This approach is due to Dieter.)