I want to construct a joint pdf for $X$ and $Y$ over the domain $\Omega_1$ and $\Omega_2$ as follows. $$ f(x,y)= \begin{cases} \dfrac{1}{2}&(x,y)\in\Omega_1\\ \dfrac{3}{2}&(x,y)\in\Omega_2\\ 0&\text{otherwise} \end{cases} $$ where the domain $\Omega_1$ and $\Omega_2$ is drawn as below:
If I try to integrate the pdf over $\Omega_1$ and $\Omega_2$, i.e. $$\iint\limits_{\Omega_1} \dfrac{1}{2} dydx + \iint\limits_{\Omega_2} \dfrac{3}{2} dydx$$ the result is $1$.
However, I doubt this function is a joint pdf because the value of the function is $\dfrac{3}{2}>1$ for $\Omega_2$.
Is this function not a joint pdf?