Select integrated circuits, test them in sequence until you find the first failure, and then stop. Let N be the number of tests. All tests are independent with probability of failure p = 0.1. Consider the condition B = {N ≥ 20}.
(a) Find the PMF PN (n).
(b) Find PN|B(n), the conditional PMF of N given that there have been 20 consecutive tests without a failure.
(c) What is E[N|B], the expected number of tests given that there have been 20 consecutive tests without a failure?