Problem #4 Suppose that the proportion of defectives shipped by a vendor, which varies somewhat from shipment to shipment, may be looked upon as a random variable having the beta distribution with a = 3 and B = 2. (a) Find the mean of this beta distribution, namely, the average proportion of defectives in a shipment from this vendor. (b) Find the probability that a shipment from this vendor will contain at most half defectives.