If X is a poisson variate such that =P(X=1)=P(X=2) , then P(X=4) is equal to

Step-by-step solution

Given X is a poisson variate such that aligned & =P(X=1)=P(X=2) & e^ - 1 ! = e^ - ^2 2 ! =2 & =P(X=1) & =e⁻² 2= 2 e^2 aligned aligned & P(X=4)= e^ - ^4 4 ! = e⁻²(2)^4 24 & = e⁻² 16 24 = 2 3 e⁻²= 1 3 aligned [from Eq. (i)]