A joint density function of the continuous random variables $x$ and $y$ is a function $f(x, y)$ satisfying the following properties.
(a) $f(x, y) \geq 0$ for all $(x, y)$
(b) $\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} f(x, y) d A=1$
(c) $P[(x, y) \in R]=\int_{R} \int f(x, y) d A$
Show that the function is a joint density function and find the required probability.
$$\begin{aligned}
&f(x, y)=\left\{\begin{array}{ll}
\frac{1}{10}, & 0 \leq x \leq 5,0 \leq y \leq 2 \\
0, & \text { elsewhere }
\end{array}\right.\\
&P(0 \leq x \leq 2,1 \leq y \leq 2)
\end{aligned}$$