Python classwork

1.  Write your own code to generate random variates from the following distributions:
a.  Exponential distribution (mean inter-arrival time of 0.25)
b.  Bernoulli distribution ( p = 0.25)
c.  Binomial distribution (n = 20, p = 0.5)
d.  Poisson distribution (arrival rate = 4.0)
Draw histograms for sequences of N random numbers for 1000, 10000 and 100000.

Poisson distribution

Here's how Wikipedia says Knuth says to do it:

init:
     Let L ← e^(−λ), k ← 0 and p ← 1.
do:
     k ← k + 1.
     Generate uniform random number u in [0,1] and let p ← p × u.
while p > L.
return k − 1.

In Java, that would be:

public static int getPoisson(double lambda) {
  double L = Math.exp(-lambda);
  double p = 1.0;
  int k = 0;

  do {
    k++;
    p *= Math.random();
  } while (p > L);

  return k - 1;
}