I got an exercise on my class about bivariat distribution. Given $f(x,y)= x+y \quad \text{for} \quad 0<x<1, 0<y<1\\ f(x,y)= 0 \quad \text{for other.}\\$ Find $P[X+Y \leq \frac{3}{2}]$.
I tried to find that by drawn the graphic first. Then this is the graphic.
After that, I evaluated the value of $P[X+Y \leq \frac{3}{2}]$ used two different ways and it gave two different values, too. My first value is $P[X+Y \leq \frac{3}{2}]=\frac{23}{24}$ The second value is $P[X+Y \leq \frac{3}{2}]=\frac{19}{24}$.
Which one is correct? My first value or the second value?
Thanks for any help.