1. Given a hypergeometric H(n, Nd,N ) random variable X for which n = 5, Nd = 2 and N = 10:

(i) Determine and plot the entire pdf, f (x) for x = 0, 1, 2, ..., 5

(ii) Determine P (X > 1) and P (X 2)

(iii) Determine P (1 ≤ X ≤ 3)

2. A crate of 100 apples contains 5 that are rotten. A grocer purchasing the crate selects a sample of 10 apples at random and accepts the entire crate only if this sample contains no rotten apples. Determine the probability of accepting the crate. If the sample size is increased to 20, ?nd the new probability of accepting the crate.