Suppose that X1∼N(0,9)X_1 \sim N(0,9)X1∼N(0,9) and X2∼N(0,16)X_2 \sim N(0,16)X2∼N(0,16) are independent. Compute E[X1∣X1+X2=5]\mathbb{E}[X_1 \mid X_1 + X_2 = 5]E[X1∣X1+X2=5].
