Each applicant has a score. If there are a total of n applicants then each applicant whose score is above sn is accepted, where s1 = 0.2, s2 = 0.4, sn = 0.5, n ≥ 3. Suppose the scores of the applicants are independent uniform (0, 1) random variables and are independent of N, the number of applicants, which is Poisson distributed with mean 2. Let X denote the number of applicants that are accepted. Derive expressions for

(a) P(X = 0).

(b) E[X].