$1\mathrm{.}22$ Consider a non$-$stationary Poisson arrival process with arrival rate function $(t).$ It is

assumed that $(t)$ is continuous and bounded in $t.$ Let $>0$ be any upper bound on the

function $(t).$ Prove that the arrival epochs of the non$-$stationary Poisson arrival process can

be generated by the following procedure:

$($a$)$ Generate arrival epochs of a Poisson process with rate $.$

$($b$)$ Thin out the arrival epochs by accepting an arrival occurring at epoch $s$ with probability

$\frac{s}{}$ and rejecting it otherwise.