I need this solution and specially explain the limit of marginal distribution. because i have a answer where tutor did not explain the limit / how he get this limit and why he use this limit. that's why i don't understand. so please explain easily

J7. Let X1, X2, and X3 be independent standard random variables. Let Y=X, and Y,= (Xi+X2)/2, and Y2= (Xi+X2+ X,)/3. Find the joint distribution of Y1, Y2, and Y, and hence the marginal distribution of Y3