If the mean of a poisson distribution is 1 3 , then the ratio P(X=1): P(X=2) is

Step-by-step solution

Given, Mean of Poisson distribution =1 / 3 For a Poisson distribution, the mean is equal to the parameter. Hence, the parameter is 1 / 3 . P(X=1)= e^ -1 / 3 (1 / 3)^1 1 ! =e^ -1 / 3 (1 / 3)P(X=2)= e^ -1 / 3 ( 1 3 )^2 2 ! P(X=1): P(X=2)= e^ -1 / 3 ( 1 3 ) e^ -1 / 3 ( 1 3 )^2 2 ! = 2 1 / 3 = 6 1 =6: 1