Question

Suppose the number of phone calls passing through a particular cellular relay system, follows a Poisson distribution with an average of 3 calls during a 1-min period.

(A) Find the probability, p, that no call will pass through the relay system during a given 2-min period.

(B) Find the probability that at least four minutes will pass before a call is passed through the relay system.

Answer 1

a)

expected calls in 2 min period =2*3 =6 calls

P(no call pass through the relay system during a given 2-min period =P(X=0)=e^-66⁰/0! =0.002479

b)

expected calls in 4 min period =4*3 =12 calls

P(no call pass through the relay system during a given 4-min period =P(X=0)=e^-1212⁰/0! =0.000006