4 Let X posses a Poisson distribution with parameter lambda

(4) Let X posses a Poisson distribution with parameter lambda. Show that P{X = i + 1}/P{X = i} = lambda/i + 1

Solution

As X is a Poisson variable, x has distribution as

P(X=k) =

Substitute X=i and i+1

Then let us find

  = /   =

Thus proved.

This is the recurrence for mula for Poisson distribution prob and lembda is replaced by l here for typing purposes.