Unless stated otherwise in the exercise, use software to find the exact Poisson.

Question 5.55

5.55 Calculator convenience.

Suppose that follows a Poisson distribution with mean .

  1. Show that .
  2. Show that for any whole number .
  3. Suppose . Use part (a) to compute .
  4. Part (b) gives us a nice calculator convenience that allows us to multiply a given Poisson probability by a factor to get the next Poisson probability. What would you multiply the probability from part (c) by to get ? What would you then multiply by to get ?

5.55

(a) .
(b)
(c) .
(d) .