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 probabity model describes the experiment: Factory Q Factory R
small order 0.3 0.2
medium order 0.1 0.2
large order 0.1 0.1

a. Find PB M(b, m), the joint PMF of the number of boxes and the distance.
b. What is E[B], the expected number of boxes?
c. Are B and M independent?