Let X1,...,Xn be a random sample from a Poisson distribution with mean theta. Find $\displaystyle E(Y_1 = X_1 + 2X_2 + 3X_3 | Y_2 = \Sigma X_i)$

I know that $\displaystyle \Sigma X_i = Pois(\theta n)$

I need to find $\displaystyle P(Y_1|Y_2) = \frac{P(Y_1,Y_2)}{P(Y_2)}$

How would I find the joint PMF of Y1 and Y2?