Consider the following algorithm for generating a random sample of size n from the set of integers {1, 2, . . . , N }. where [I s: n s: N. 1 SampleiN, it}: 2 I = 3 chosen = {} if chosen is a set of distinct integers, initially on envisager set 4 while |chosen| 4:: n: 5 I += 1 H I is counting the total number of rolls of the die 5 chosen.add{Flol'LDie{NH if if the roll of the die [which is random in I . .. N] F H is not in chosen, then add it to chosen. 3 return chosen {a} [9 Points] Let the random variable I; be the number of rolls it takes From the time the chosen set has il values to the first time a new value is added {i.e., the chosen set has i values]. What type of random variable From our zoo is I; and what isfare the relevant parameter(s]? What is I in terms of the random variables 1;? Calculate E[I] in terms of N and the harmonic numbers Hm [m E 1]. Recall that andliorklwrzl: is 1 1 1 1 HH= = - 1 l\" '" r+l+r+2+ +k .21: ll t=r+l (b) [15 Points] What is Vol-{I}? You can leave 1your answer in summation form