We do plenty of math, so I’d like to test out MathJax support.

Here is an example of MathJax inline rendering — $ 1/x^{2} $. And here is a block rendering:

$$r_{XY} = frac{mathrm{cov}(X,Y)}{sqrt{mathrm{var}(X)mathrm{var}(Y)}}$$

Now, if we’d like to get serious, we’d do something involving multiline aligned equations, like

$$% <![CDATA[ begin{align} mathcal{N}(t, mu, sigma) &= mathrm{normal} newline &= frac{1}{sqrt{2 pi} sigma} e^{-frac{(t-mu)^2}{2 sigma^2}} end{align} %]]>$$

or even an inline formula like $ sum_{t=0}^{infty} frac{x^t}{t!} = e^x$.

Or we could try defining a command, like this. $ newcommand{water}{mathrm{H}_{2}mathrm{O}} $

Buffer slides off the sides of our tubes like $water$ off a duck’s back.

Or a more fancy set of equations:

$$% <![CDATA[ begin{align} mbox{Union: } & Acup B = {xmid xin A mbox{ or } xin B} \ mbox{Concatenation: } & Acirc B = {xymid xin A mbox{ and } yin B} \ mbox{Star: } & A^star = {x_1x_2ldots x_k mid kgeq 0 mbox{ and each } x_iin A} \ end{align} %]]>$$

Or to write the case likelihood function of PLCM model (Wu et al. 2015):

$$Pr(boldsymbol{M}_i mid I_i=1) = sum_{ell=1}^Lpi_elltheta_ell^{M_{iell}}(1-theta_ell)^{1-M_{iell}}prod_{jneq ell}psi_j^{M_{ij}}(1-psi_j)^{1-M_{ij}}$$

One can also use some doses of number theory…

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