1. The problem statement, all variables and given/known data X1 ∼ N(μ1,σ12) and X2 ∼ N(μ2,σ22) Let Y = X1 + X2 Find the p.d.f. of Y & label the distribution. 2. Relevant equations 3. The attempt at a solution Not quite sure how to go about this problem. µY=E[Y]=E[X1+X2]=E[X1]+E[X2]=µ1+µ2 σY2=E[Y2] - µY2 E[X12+ 2X1X2 +X22] - (µ1+µ2)2 I think that might be how you start it. Feel free to correct me and start over or continue. Thanks.