3. (10%) A random variable X has a Poisson distribution with λ > 0. Given X, a random variable Y is N(μ, X).

(a) (5%) What is the E(XY)?
(b) (5%) What is the \(\operatorname{Var}(\mathbf{Y})\)? (HINT: \(\operatorname{Var}(\mathbf{Y}) = \operatorname{E}(\mathbf{Y}^2) - \operatorname{E}(\mathbf{Y})^2\)

(Please show the process of calculation)