2.65 A communication channel can carry up to 10 messages at a time. The channel capacity is designed assuming that the number of messages to be transmitted at any given time is Poisson distributed with a mean of 5. (a) What is the probability that a message cannot be transmitted because the channel is busy? (b) What is the probability distribution of the actual number of messages transmitted at any given time? What is the expected value of this distribution? (Hint: This is a truncated Poisson distribution conditional on the number being less than or equal to 10.)