A manufacturing company produces two types of phones; radio phones and plain phones and ships them out in boxes. Each box contains two phones of the same type. Every week, a quality control technician randomly selects a shipping box, records the type of phone in the box (radio or plain), and then tests the phones and records the number that were defective. It was determined that the probabilities of obtaining 0, 1 and 2 defective(s) for the radio phones were respectively 0.45, 0.07 and 0.01, while for the plain phones, the probabilities were respectively 0.37, 0.08 and 0.02. Required:
Assume that we define a random variable N to be the number of defective phones within a randomly chosen box. Calculate the mean and variance of the random variable N.