Telephone calls coming into a busy switchboard follow a Poisson distribution witha rate of 3 per minute. The switchboard, however, can answer at most 4 calls in a oneminuteinterval, any calls exceeding 4 during that period receive a busy signal.a) What is the probability that there will be no incoming call to this switchboard inthe next 30 seconds?b) Let Y denote the number of calls answered in a one-minute period. Find the pdf ofY and E(Y).