"X is distributed as ..." notation A question about notation:
We sometimes use $\sim$ to denote "distributed as" e.g. if $X$ is Gaussian we write $X \sim N(\mu, \sigma^2)$. 
Is it acceptable to use the "~" notation for an arbitrary distribution? e.g. can we write 
$$X \sim \begin{cases} \frac{3}{2}x^2, & x \in [-1,1] \\0 & \text{otherwise} \end{cases}$$
If not, is there another way to write "$X$ is distributed as ..."? i.e. without the more verbose "Let $p_X(x)$ be the pdf of $X$. Then $p_X(x)=$ ...

From what I've seen, I think it's more common to write 
$$X\sim \frac32x^2I(-1\le x\le 1)\color{red}{dx}$$
in your case. 
