This exercise obtains a useful identity for the cdf of a Poisson cdf.
(a) Use Exercise 3.3.5 to show that this identity is true:
for λ > 0 and n a positive integer.
This demonstrates the relationship between the cdfs of the gamma and Poisson distributions.
(b) Obtain the identity used in Example 4.3.3, by making the transformation z = λx in the above integral.