Materials/supplies are delivered from two different distributers into a manufacturing site. In each day there is a 30% chance of delivery from distributer A, 40% chance of delivery of distributor B and 30% chance of no delivery at all independent of any other day. We can assume that the delivery from the two distributers are also independent. a. Find the probability that there are 5 deliveries in one week (7 days). b. If in day 2 there was a delivery from distributer A, find the average time of receiving two more deliveries from this distributer. c. If in day 2 there was a delivery from distributer A, find the average time of receiving two more deliveries. d. X is the number of items delivered by distributor A before distributer B delivers 3 items. Find the PMF of X.