Consider a Poisson process with intensity $(x)=40sin(2x)$ on the interval $D=[0,\frac{}{2}]$ and $0$ otherwise.

a$)$ How many points are expected to be in a random sample from this process?

b$)$ Write a computer program to generate one sample corresponding to this Poisson process, and provide some plot$($s$)$ or other outcome$($s$)$ of

this program.

Penalty: Part b$)$ can be solved using either an efficient algorithm that generates the random sample directly, or some variation of a more

inefficient rejection$-$type algorithm $($such as the thinning method studied in classes$).$ In order to earn full marks in this question, it is required

that you do not use a rejection$-$type algorithm. This means that you will be penalized if you use some rejection algorithm.