Question: (a) Write a Mathematica command to simulate a desired number of arrival times (T_{1}, T_{2}, ldots) of a Poisson process with a desired rate (lambda).

(a) Write a Mathematica command to simulate a desired number of arrival times $T_{1}, T_{2}, \ldots$ of a Poisson process with a desired rate $\lambda$.

(b) Write a Mathematica command that accepts a list of arrival times and a particular time $t$, and returns the value of $N_{t}$.

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