# How to find this probability of these 2 continuous variables?

Problem.1) The joint probability density function of two continuous random variables $$X$$ and $$Y$$ is given by

$$f(x) = \begin{cases} \frac{1}{8}(x+y), & \text{for } 0 \leq x \leq 2, 0 \leq y \leq 2\\ 0, & \text{otherwise} \end{cases}$$

Calculate $$\mathbf{P}(X + Y \leq 2)$$.

1) The original image can be seen in https://i.stack.imgur.com/Xbmhq.jpg

• thank you all, I am wtill not good at this. – Sergio Jun 30 at 11:08

$$P(X+Y\leq 2)=\int_0^{2}\int_0^{2-x} \frac 1 8 (x+y)dydx=\frac 1 8 \int_0^{2} [x(2-x)+\frac {(2-x)^{2}} 2] dx$$. Can you continue?