Question: 1. Interarrival times (in minutes) for fax messages on a terminal are independent, exponential (λ = 0:1). This means the time X for the arrival of the fourth message is gamma(4, 0.1). Without using tables or m programs, utilize the relation of the gamma to the Poisson distribution to determine P (X ≤ 30).
2. Customers arrive at a service center with independent interarrival times in hours, which have exponential (3) distribution. The time X for the third arrival is thus gamma (3; 3). Without using tables or m-programs, determine P (X ≤ 2).