Originally Posted by

**garryp** From the given domain of X and Y it is clear that X + Y is defined over 0 to 3.

but since Y is defined only on 0 to 1 and X is only defined on 0 to 2 we have to break our calculation in intervals (0,1), (1,2) and (2,3).

now calculating F(Z = a) where Z = X + Y

Case 1: when a is between 0 to 1.

F(a) = P(X+Y<a) = area under X + Y (and since a is less than 1 the overall area will be area between (0,0), (0,a) and (a,0).

To calculate it we can integrate it with following limits:

int(a,0)int(a-y,0) f(x)f(y) dx dy

now differentiating it will give the pdf of (X+Y) for 0<a<1

Case2: when a is between 1 to 2.

Case3: when a is between 2 to 3.

For case 2 and 3, I am not able to understand how to set the limits. This is what I wanted to understand.