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?
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
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