aez-notes

A bread salesman sells on the average 20 cakes on a round of his route. What is the chance that he sells an even number of cakes? (We assume the sales follow the Poisson distribution.)

Maxima can compute the probability of an even number under a Poisson distribution, but we need the exponentialize function to put this in a form that makes the expression easy to read.

load(simplify_sum)$
load(distrib)$

f(x) := pdf_poisson(x,m);

print(
  expand(
    exponentialize(
      simplify_sum(sum(f(2 * i), i, 0, inf))
      )
    )
  );

/*

  - 2 m
%e        1
------- + -
   2      2

*/

For \(m \approx 20\) this is very close to \(1/2\).