Compute the probabilities of the following events? homework help

Question

 

Assume that the number of messages input to a communication channel in an interval of duration t

seconds is Poisson distributed with parameter 0.3t.  Compute the probabilities of the following 

events: 

(a) Exactly two messages will arrive during a five-second interval, 

(b) At most eight messages arrive in a period of ten seconds, 

(c) The number of message arrivals in an interval of duration twenty seconds is between eight and 

twelve.