Consider a Poisson random variable X with parameter λ = 2.
a. Find the probability that X is within one standard deviation of its mean.
b. Find the probability that X is within two standard deviations of its mean.
c. Find the probability that X is within three standard deviations of its mean.
d. Do the empirical rules we learned previously seem to be applicable in working with the Poisson distribution where λ = 2? Explain why or why not.
e. Repeat parts a through d for the case of a Poisson random variable where λ = 20.