Wars. In the paper “The Distribution ofWars 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.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Wars. In the paper “The Distribution ofWars 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
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.
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