LaTeX

Within R markdown (within RStudio), we can use the LaTeX language to create beautiful mathematical equations. Here are some examples to work through.

The helpful $ and $$
If I type $f_X(x)$ in a body of text, it produces \(f_X(x)\). Notice that this LaTeX text is started by $ and ended by $. With just 1 $ on either end, the formula remains in my body of text. If I want it to appear on its own in the center of the page I use $$ on either end. For example, $$f_X(x)$$ gives \[f_X(x)\]

Basic features

• probability & counting stuff

  code	result
  $P(A)$	\(P(A)\)
  $P(A \cap B)$	\(P(A \cap B)\)
  $P(A \cup B)$	\(P(A \cup B)\)
  $P(A|B)$	\(P(A|B)\)

  
  

  More complicated is the “choose” notation:

  $\left(\begin{array}{c} n \\ x \end{array} \right)$

  <>

  Gives \[\left( \begin{array}{c} n \\ x \end{array} \right)\]

• subscripts

  code	result
  $x_2$	\(x_2\)
  $x_10$	\(x_10\)
  $x_{10}$	\(x_{10}\)

• superscripts

  code	result
  $x^2$	\(x^2\)
  $x^10$	\(x^10\)
  $x^{10}$	\(x^{10}\)

• fractions

  code	result
  $\frac{1}{2}$	\(\frac{1}{2}\)
  $\frac{a+1}{b+0}$	\(\frac{a+1}{b+0}\)

• integrals

  code	result
  $\int f(x) dx$	\(\int f(x) dx\)
  $\int_0^1 f(x) dx$	\(\int_0^1 f(x) dx\)
  $\int_{-1}^{10} f(x) dx$	\(\int_{-1}^{10} f(x) dx\)
  $\int_{-\infty}^\infty f(x) dx$	\(\int_{-\infty}^\infty f(x) dx\)

Multi-line equations

One of many ways to present a multi-line equations is by using split. In the examples below, notice the following:

• start with \begin{split} and end with \end{split}
  
• indicate the end of each line in the equation by \\
  
• use & to indicate the point at which to line up the lines

This code

produces

\[\begin{split} x & = 1 \\ y & = 2 \\ \end{split}\]

This code

produces

\[\begin{split} P(A|B) & = \frac{P(A \cap B)}{P(B)} \\ & = \frac{P(B|A)P(A)}{P(B)} \\ \end{split}\]