Given that x is a random variable, for which a Poisson probability distribution provides a good approximation, use Table III in Appendix A to compute the following:

a. P(x ≤ 2) when λ= 1

b. P(x ≤ 2) when λ= 2

c. P(x ≤ 2) when λ = 3

d. What happens to the probability of the event {x ≤ 2} as λ increases from 1 to 3? Is this intuitively reasonable?