If the mean of a poisson variate (X ) is 1 , then ( _ r=0 ^ |r-1| P(X=r)= )

Step-by-step solution

It is given that mean of a poisson variate (X ) is ( = l ), ( aligned P(X & =r)= e^ - ^r r ! = e⁻¹ r ! & _ r=0 ^ |r-1| P(X=r)= _ r=0 ^ |r-1| e⁻¹ r ! & =e⁻¹ [ 1 0 ! + 0 1 ! + 1 2 ! + 2 3 ! + . . ] & =e⁻¹ (1+ 1 2 ! + 2 3 ! + . . . )=e⁻¹(1+1)= 2 e aligned ) Hence, option (c) correct.