How to use LaTeX math formulas on blogspot

This is not a post, it's a sandbox. I try out math formulas here to see if they work. The reason is that the preview feature of blogger doesn't parse LaTeX.

On Blogspot, I can use MathJax, which produces beautiful math formulas. (That's why I switched from Wordpress, where the formulas are super ugly.)

Let's have a simple formula, say $x=0$, and let's also try something complicated like $\sum_{k=0}^\infty \frac{1}{k^2}$. Ok.

What about displaystyle?
$$ \int_{-\infty}^\infty e^{-x^2} \, dx. $$

What about aligned things:
$$ \begin{aligned}
x&=y & a&=b \\
u&=v & c&=d &\text{and with a text, too.}\\
Did that work, too?

For $j=1,\dots,n$ and $t\ge 0$, let $X_j(t)$ be 0 if bin $j$ is empty after the $t$th ball has been thrown, and 1 if it is non-empty. Let $$ \begin{aligned} X(t) &= \sum_{j=1}^n (1-X_j(t)) &&\text{the number of empty bins after the $t$th ball has been thrown, and}\\ Y(t) &= \sum_{j=1}^n X_j(t) &&\text{the number of non-empty bins after the $t$th ball has been thrown.}\\ \end{aligned} $$ $$ \begin{aligned} \mathbb{E}X(t) &= n(1-\tfrac{1}{n})^t \\ \mathbb{E}Y(t) &= n\Bigl( 1 - (1-\tfrac{1}{n})^t )\\ \end{aligned} $$