At tiem t = 0, you begin counting the arrivals of buses at a depot. The number of buses Ki that arrive between time i - 1 minuts and time i minutes has the poisson PMF

K1,K2, . . . are an iid random sequence. Let Ri = K1 + K2 + ˆ™ ˆ™ ˆ™ + Ki denote the number of buses arriving in the first i minutes.
(a) What is the moment generating function Ï•Ki (s)?
(b) Find the MGF Ï•Ri(s).
(c) Find the PMF PRi(r).
(d) Find E[Ri] and Var[Ri].

Transcribed Image Text:

[2e-2/kl k=0, 1,2, . . . , otherwise. (k) = 0