(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..