Question

a. Given an arrival process with λ= 8.0, what is the probability that an arrival occurs in the first t = 7 time units?

solution a: f(t)=8*e^(-8t)F(t)=1-e^(-8t), P(T<=7)=F(7)

b. Given an arrival process with λ= 5.0, what is the probability that an arrival occurs after t = 5 time units?

solution b: f(t)=(1/5)*e^(-t/5), F(t)=1-e^(-t/5)

I don't understand the difference between these solutions, which take 8 and 1/5 respectively. Shouldn't solution b equals: f(t)=5*e^(-5t)? Can someone explain with details to me?

Answer 1

The CDF provided is incorrect since 5.0 is the value of the rate parameter not the value of mean arrivals. If we have given the mean arrivals we used (1/0.5).

Therefore the probability that an arrival occurs after t=5 time units is given by