Question

N students throw their ID cards into a bag, which is then thoroughly mixed. The students are then (al at once) randomly assigned IDs, with each student equally likely to get any of the N IDs a) Determine the expected number of students that get their own ID (Hint: Define a suitable binary random variable X for each student i.). (10 Points) b) Suppose now instead that, one at a time, students reach into the bag to get ID, with V a new the number of IDs in the bag thus diminished until the last student picks the single remaining ID. For this case, determine the expected number of students that get their own IDs. (10 Points)

Answer 1

a e ith stu dent Xi-.p E()= E)= X. b Trent that ith student anus id N-I N-2 N-3 So, PCY=ti) N-IN-2 50, EY:)= N 50, E(Y)=I. (Ana).