Indeed Suppose: X ~ Poi(Y) , here Y is the parameter and assume Y is also a RV and follows a distribution, then E(X/Y=y)=y - Hope you agree with this, since 'y' is mean of the poission dist. E(X)=E(E(X/Y)) = E(Y) , which is equal to the mean of Y distribution. Thanks & Regards, Nagesh.
