$2.(40$ pts$)$ Consider a non$-$homogenous Poisson process with the rate function below.

$0235679$

t $($hours$)$

$0$

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$\backslash$lambda $($t$)($count$/$hour$)$

rate function of a non$-$homogenous Poisson process

$($a$)(10$ pts$)$ What is the distribution for the number of events between t $=2$ and t $=6?$

$($b$)(10$ pts$)$ According to the distribution you found in the last part, what is the probability

of no events between t $=2$ and t $=6?$

$($c$)(20$ pts$)$ How would you simulate entity arrivals from this process in Arena? State the

relevant module$($s$)$ and give the details to be entered.