# Question: Consider a Poisson random variable X with parameter

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.

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.

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