If X is a poisson variable such that 3 P(X=4)= 1 2 P(X=2)+P(X=0) , then the mean X is

Step-by-step solution

Given, 3 P(X=4)= 1 2 P(X=2)+P(X=0) X is poisson distribution this gives P(X=x)= e^ - ^x x ! , [x=0,1,2, ] Now, 3 P(X=4)= 1 2 P(X=2)+P(X=0) aligned & 3 e^ - ^4 4 ! = 1 2 e^ - ^2 2 ! + e^ - ^0 0 ! & 3 ^4 4 ! = ^2 4 +1 & ^4 8 = ^2 4 +1 or ^4-2 ^2-8=0 aligned Let ^2=u , then u^2-2 u-8=0 Gives, u=4,-2 array ll & ^2=4 & =2 array [ ^2 -2 ] Mean of X=2