This function returns a random variate from the Poisson distribution with mean mu. The probability distribution for Poisson variates is,
for \(k \geq 0\).
This function computes the probability \(p(k)\) of obtaining \(k\) from a Poisson distribution with mean mu, using the formula given above.
These functions compute the cumulative distribution functions \(P(k), Q(k)\) for the Poisson distribution with parameter mu.