Category: Math

WordPress does LaTeX

John Candlish

My February '95 Statistics 462 midterm notes.  In LaTeX.

$ {\bf Independence} $

$ P(A \cap B) = P(A) \cdot P(B) $

$ f_{X_1,X_2,\ldots,X_n}(x_1,x_2,\ldots,x_n)=f_{X_1}(x_1)f_{X_2}(x_2)\cdots f_{X_n}(x_n) $

$ P((X,Y)\in R)={\displaystyle {\int\!\!\!\int}_{R}} f_X(x)f_Y(y)dy\;dx $

$ {\bf Moment \: Generating \: Function} $

$ M_X(t)=E(e^{tX}) $

$ E(X)=M_{X}^{'}(0); \quad E(X^2)=M_{X}^{''}(0) $

$ Var(X)=M_{X}^{''}(0)-[M_{X}^{'}(0)]^2 $

$ {\displaystyle \bar{Y}=\frac{1}{n}\sum_{i=1}^{n}Y_i\quad Var(\bar{Y})=\frac{Y_1}{n}} $

$ {\bf Chebyshev's \: Inequality }$

$ {\displaystyle P(|X-\mu| \geq \epsilon ) \leq \frac{\sigma^2}{\epsilon^2} = \frac{Var(X)}{\epsilon^2} }$

$ {\bf Special \: Distributions } $
$ {\rm Binomial \: Distribution} $

$ X \sim b(n,p) \Rightarrow P(X=K)={\displaystyle {n \choose k }}p^k(1-p)^{n-k} $

$ E(X)=np \quad Var(X)=npq $

$ {\rm Poisson \:Limit}$

$ {\displaystyle \lim_{n \rightarrow \infty } { n \choose x }p^x(1-p)^{n-x} = \frac{e^{-\lambda}\lambda^x}{x!}} $

$ {\rm Poisson \: Distribution} $

$ X \sim P(\lambda) \Rightarrow P(X=k)=\frac{e^{-\lambda}\lambda^k}{k!} $

$ E(X)=\lambda \quad Var(X)=\lambda $

$ \mbox{MLE for }\lambda = \bar{X} $

$ {\rm Poisson \: Approximation} $

$ \mbox{If }X \sim b(n,p) \mbox{ then } {\displaystyle P(X\geq K) \doteq \sum_{i=k}^{\infty} \frac{e^{-np}(np)^k}{k!} }$

$ {\rm Normal \: Distribution} $

$ X \sim N( \mu, \sigma^2 ) \Rightarrow P( a < X < b ) = {\displaystyle \frac{1}{\sqrt{2\pi}\sigma} \int_{a}^{b}e^{\frac{-1}{2}[(x-\mu)/\sigma]^2} dx} $

$ X \sim N(\mu,\sigma^2)\quad \Rightarrow \quad{\displaystyle \frac{X-\mu}{\sigma}}\sim N(0,1) $

$ \hat{\mu}={\displaystyle \frac{1}{n}\sum_{i=1}^{n}}y_i=\bar{y} \quad\quad\quad \hat{\sigma}^2={\displaystyle \frac{1}{n}\sum_{i=1}^{n}}(y_i-\bar{y})^2 $

$ Y_1+Y_2\sim N(\mu_1+\mu_2,\sigma_1^2+\sigma_2^2) $

$ \mbox{If }{\displaystyle \bar{Y}=\frac{1}{n}\sum_{i=1}^{n}Y_i} \quad\mbox{then } {\displaystyle \bar{Y} \sim N(\mu,\frac{\sigma^2}{n}}) $

$ {\rm DeMoivre-Laplace} $

$ \mbox{If }X \sim b(n,p) \mbox{ then } \lim_{n \rightarrow \infty} P \left( c < {\displaystyle \frac{X-np}{\sqrt{npq}}}< d \right) = P \left( c<Z<d \right) $

$ {\bf Consistancy} $

$ P(|W_n-\theta| < \epsilon ) > 1-\delta \quad n>n(\epsilon,\delta) $

$ \mbox{let }\delta = {\displaystyle \frac{Var(W)}{\epsilon^2}} \mbox{ and use Chebyshev to find } n $

$ {\bf pdfs \: of \: Common \: Estimators} $

$ \mbox{uniform distribution} $

$ Y_{max} \:\:\:\:\:\:f_W(w;\theta)={\displaystyle \frac{nw^{n-1}}{\theta^n}} $

$ Y_{min} \:\:\:\:\:\:f_W(w;\theta)={\displaystyle \frac{n}{\theta}\left(1-\frac{y}{\theta}\right)^{n-1}} $

$ {\bf MLE } $

$ \mbox{likelyhood function} $

$ L(\theta)={\displaystyle \prod_{i=1}^{n}}f_Y(y_i;\theta) \quad \Rightarrow \quad \ln L(\theta)={\displaystyle \sum_{i=1}^{n}}\ln f_Y(y_i;\theta) $

$ \mbox{solve } \quad 0 =\frac{\partial}{\partial\theta} {\displaystyle \sum_{i=1}^{n}}\ln f_Y(y_i;\theta) $

$ {\bf CI} \: 100(1-\alpha)\% \mbox{ for the binomial parameter } p $

$ {\displaystyle \left( \frac{y}{n}-z_{\alpha/2}\sqrt{\frac{\frac{y}{n} \left(1-\frac{y}{n}\right)}{n}},\frac{y}{n}+z_{\alpha/2}\sqrt{\frac{\frac{y}{n} \left(1-\frac{y}{n}\right)}{n}} \right) }$

$ \quad\mbox{where}\quad {\displaystyle y=\sum_{i=1}^{n}X_i } $

So yes, WordPress does LaTeX, but it is finicky and missing a lot of functionality. If you try to use LaTeX that doesn’t work inside the math environment (such as begin{align} ... end{align}), it wont parse.  Also, you need to use the displaystlye keyword judiciously.

Edit: I've uninstalled JetPack and so lost its Beautiful Math feature.   Therefore I've installed the WP LaTeX plugin. It is more configurable, and can offload formatting to a real LaTeX running alongside WordPress.  With a little hacking I've got {align} going. Why someone thought is was sensible to limit WordPress' LaTeX support to the math environment is beyond me.

One requirement of the WP LaTeX plugin is that the WP unformatted plugin is also installed, so that the wptexturize() function can be disabled on LaTeX posts.