From a recent statistical analysis for the last five years o

From a recent statistical analysis for the last five years, on an average there are 4 (major) air accidents per month in the world. Let X be the number of air accidents occurred in a randomly selected month. It is known that X ~ Poisson(l) approximately, where the intensity l » 4 accidents (monthly average number of accidents). Find the probability that there will be 4 or more air accidents

in a given month of the next year; Hint: The required probability is P(X ³ 4).

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials

Mean = = 4 (major) air accidents per month in the world

P( X < 4) = P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= e^-4 * 2 ^ 3 / 3! + e^-4 * ^ 2 / 2! + e^-4 * ^ 1 / 1! + e^-4 * ^ 0 / 0!
= 0.4335
P( X > = 4 ) = 1 - P (X < 4) = 0.5665