In the paper "The Distribution of Wars in Time" (Journal of the Royal Statistical Society, Vol. 107, No. 3/4, pp. 242-250), L. F. Richardson analyzed the distribution of wars in time. From the data, we determined that the number of wars that begin during a given calendar year has roughly a Poisson distribution with parameter λ = 0.7. If a calendar year is selected at random, find the probability that the number, X, of wars that begin during that calendar year will be
a. Zero.
b. At most two.
c. Between one and three, inclusive.
d. Find and interpret the mean of the random variable X.
e. Determine the standard deviation of X.