34. Let X be a Poisson random variable with parameter . Show that the maximum of P(X = i) occurs at [], where [] is

34. Let X be a Poisson random variable with parameter λ. Show that the maximum of P(X = i) occurs at [λ], where [λ] is the greatest integer less than or equal to λ.

Hint: Let p be the probability mass function of X. Prove that

Use this to find the values of i at which p is increasing and the values of i at which it is decreasing.

p(i) = p(i 1).