A company receives shipments from two factories. Depending on the size of the order, a shipment can be in
1 box for a small order,
2 boxes for a medium order,
3 boxes for a large order
The company has two different suppliers: Factory Q is 60 miles from the company. Factory R is 180 miles from the company. An experiment consists of monitoring a shipment and observing B, the number of boxes, and M, the number of miles the shipment travels.
The following probability model describes the experiment:
(a) Find PB,M (b, m), the joint PMF of the number of boxes and the distance. (You may present your answer as a matrix if you like.)
(b) What is E[B], the expected number of boxes?
(c) What is PM|B(m|2), the conditional PMF of the distance when the order requires two boxes?
(e) Are the random variables B and M independent?
(f) The price per mile of sending each box is one cent per mile the box travels. C cents is the price of one shipment. What is E[C], the expected price of one shipment?