Question

2 A PaRer by L.F. Richaideon Pu blished in the Joumal of the Royal suatistical Society orol忙cd thè distribution af wars over time ad Concluded that wars that begin ing a colender year hod a poisoan distriaion wth parameter2-o.0t, what is the Probability tha there will be at least two wars daring a given Clender year

Answer 1

Let X is a radnom vaiable shows the number of wars during a calender year. Here X has Poisson distribution with following pdf:

Let X is a random variable shows the number of wars during a calendar year. Here X has Poisson distribution with following pdf: P(X = x) = e^-0.07 0.07^x/x!, x = 0, 1, 2, ... The probability that there will be at least 2 wars during a calendar year is P(X greaterthanorequalto 2) = 1 - P(X lessthanorequalto 1) = 1 - sigma^1 _x = 0 e^-0.07 0.07^x/x! = 1 - 0.99766 = 0.00234

The probability that there will be at least 2 wars during a calender year is

$P(X\geq 2)=1-P(X\leq 1)=1-\sum_{x=0}^{1}\frac{e^{-0.07}0.07^{x}}{x!}=1-0.99766=0.00234$