Latex terms

#concept-pamphlet

What is the LaTeX code for the greater than or equal to symbol? ? \geq

$$\ge$$

What is the LaTeX code for the less than or equal to symbol? ? \leq

$$\le$$

What is the LaTeX code for the not equal to symbol? ? \neq

$$\ne$$

What is the LaTeX code for the approximately equal to symbol? ? \approx

$$\approx$$

What is the LaTeX code for the tilde symbol? ? \sim

$$\sim$$

What is the LaTeX code for the right arrow symbol? ? \Rightarrow

$$\Rightarrow$$

What is the LaTeX code for the square root of 42? ? \sqrt{42}

$$\sqrt{42}$$

What is the LaTeX code for the infinity symbol? ? \infty

$$\infty$$

What is the LaTeX code for this symbol?

$$\lambda$$

? \lambda

What is the LaTeX code for these symbols?

$$\mu ,\sigma$$

? \mu, \sigma

What is the LaTeX code for this symbol?

$$\Phi (0)$$

? \Phi(0)

What is the LaTeX code for the this symbol?

$$\Sigma$$

? \Sigma

What is the LaTeX code for this symbol?

$$\theta$$

? \theta

What is the LaTeX code for the bar X and hat X symbols?

$$\bar{X},\hat{X}$$

? \bar{X}, \hat{X}

What is the LaTeX code for the dots here:

$$1,2,\cdots ,n$$

? \cdots

What is the LaTeX code for verbatim text ‘my_function()‘? ? \verb|my_function()|

\verb|my_function()|$$ What is the LaTeX code for a fraction with units in the numerator and denominator? [[SR/memory/QchY6zuS.md|?]] `\frac{1}{1}`

\frac{1}{2}$$

What is the LaTeX code for summation from i equals 0 to n? ? \sum_{i=0}^{n} i

What is the LaTeX code for product from i equals 0 to n? ? \prod_{i=0}^{n} i

What is the LaTeX code for the probability of A intersect B? ? P(A \cap B)$$ P(A \cap B)

What is the LaTeX code for the probability of A union B? [[SR/memory/esrvx3Cj.md|?]] `P(A \cup B)` $$P(A \cup B)

What is the LaTeX code for the binomial coefficient? ? \binom{n}{k}

^This is n! / ( k! (n-k)! ). Also pronounced “n choose k”. Also seen as C(n,k)

What is the LaTeX code for the conditional probability of A given B complement? ? P(A|B^C)$$ P(A|B^C)

$$ComplementisallprobabilitiesnotinBWhatistheLaTeXcodefortheprobabilityofmeowgivencat??‘P(\text{meow }|\text{ cat})‘$$

P(\textrm{meow } | \textrm{ cat})

$$WhatistheLaTeXcodefortheprobabilityofaconditionlessthanorequalto5.0?[[SR/memory/QRyIO7M5.md|?]]‘P(\text{cond}\le 5.0)‘$$

P(\textrm{cond} \leq 5.0)

$$WhatistheLaTeXcodeforAtimesB??‘A\times B‘$$

A \times B

$$<!--LEARN:vFkjP8LQ-->WhatistheLaTeXcodeforaNormalrandomvariableXwithmean0andvariance1?[[SR/memory/4lsf24FV.md|?]]‘X\sim \mathcal{N}(\mu =0,{\sigma }^2=1)‘$$

X \sim \mathcal{N}(\mu = 0, \sigma^2 = 1)

$$WhatistheLaTeXcodeforanintegralfrom-1to1ofxsquareddx?[[SR/memory/MgaWmCD5.md|?]]‘{\int }_{-1}^1{x}^{2}dx‘$$

\int_{-1}^{1} x^2 - 2x + 1 dx

$$WhatistheLaTeXcodefortheevaluationoftheintegralfrom-1to1ofxsquareddx,withbrackets?[[SR/memory/4wwLZBzU.md|?]]‘{\left[x^2\right]}_{-1}^1‘$$

\left[ x^2 \right]_{-1}

$$WhatistheLaTeXcodeforadoubleintegral?[[SR/memory/LOzxRljX.md|?]]‘\iint ‘‘{\iint }_0^{1}xydydx‘$$

\iint_{0}^{1} xy dy dx$$ What is the LaTeX code for the evaluation of a double integral? ? \left. expression \right|_{0}^{1} Example:\left. \frac{3}{4}y^2 \right|_{-1}^{x}`

$${\frac{2}{3}y|}_{-1}^x$$

What is the LaTeX code for a 2x2 matrix with elements a, b, c, and d?

$$\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$$

? \begin{bmatrix} a & b \\ c & d \end{bmatrix} What is the LaTeX code for the correlation coefficient?

$$\rho$$

? \rho

What is the LaTeX code for a group of equations aligned? ? \begin{align*, &=, \\, end{align*} Example:

\begin{align*} 
P(X=x|Y=1,W=P_1)  &= \frac{P(X=x,Y=1 | W=P_1)}{P(Y=1|W=P_1)} \\ 
&= P(X=x|W=P_1) \\ 
&= \binom{5}{x}(0.1)^x(0.9)^{5-x} \\ 
P(X=x|Y=1,W=P_2)  
&= \frac{P(X=x,Y=1 | W=P_2)}{P(Y=1|W=P_2)} \\ 
&= P(X=x|W=P_2) \\ 
&= \binom{5}{x}(0.1)^x(0.9)^{5-x} 
\end{align*}

$$\begin{array}{rl}P(X=x|Y=1,W=P_1)& =\frac{P(X=x,Y=1|W=P_1)}{P(Y=1|W=P_1)}\\ & =P(X=x|W=P_1)\\ & =\left(\genfrac{}{}{0ex}{}{5}{x}\right)(0.1{)}^x(0.9{)}^{5-x}\\ P(X=x|Y=1,W=P_2)& =\frac{P(X=x,Y=1|W=P_2)}{P(Y=1|W=P_2)}\\ & =P(X=x|W=P_2)\\ & =\left(\genfrac{}{}{0ex}{}{5}{x}\right)(0.1{)}^x(0.9{)}^{5-x}\end{array}$$

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Other cards that are cool but don’t need to be reviewed §

What is the LaTeX code for a Bernoulli random variable X with parameter p?

X \sim \textrm{Ber}(p)

$$X\sim \text{Ber}(p)$$

What is the LaTeX code for a Binomial random variable X with parameters n and p?

X \sim \textrm{Bin}(n,p)

$$X\sim \text{Bin}(n,p)$$

What is the LaTeX code for a Poisson random variable X with lambda equal to 0?

X \sim \textrm{Poi}(\lambda=0)

$$X\sim \text{Poi}(\lambda =0)$$

What is the LaTeX code for an Exponential random variable X with lambda equal to 0?

X \sim \textrm{Exp}(\lambda=0)

$$X\sim \text{Exp}(\lambda =0)$$

What is the LaTeX code for a Beta random variable theta with parameters a and b?

\theta \sim \textrm{Beta}(a,b)

$$\theta \sim \text{Beta}(a,b)$$

What is the LaTeX code for a double integral from 0 less than y less than x less than 1 of x over y dy dx?

\iint_{0<y<x<1} \frac{x}{y} dy dx

$${\iint }_{0<y<x<1}\frac{x}{y}dydx$$

What is the LaTeX code for the evaluation of a double integral from 0 less than y less than x less than 1 of x over y dy dx?

\left. \frac{2}{3}y - \frac{3}{4}y^2 \right|_{-1}^{x}

$${\frac{2}{3}y-\frac{3}{4}{y}^2|}_{-1}^x$$

What is the LaTeX code for the variance of X?

\textrm{Var}(X)

$$\text{Var}(X)$$

What is the LaTeX code for the covariance of X and Y?

\textrm{Cov}(X,Y)

$$\text{Cov}(X,Y)$$

Latex playground §

equation editor: https://editor.codecogs.com/ cheatsheet: https://wch.github.io/latexsheet/latexsheet.pdf another cheatsheet: (source) latex cheatsheet.pdf

> [!theorem] Title
> 
> Content

> [!corollary]
> 
> Content

Title

Content

Title

Content

> [!thm] Title
> 
> Content

> [!cor]
> 
> Content

Title

Content

Note

Content> [!thm] Title Content

Note

Content

Environment name	Alias
axiom	axm
definition	def
lemma	lem
proposition	prp
theorem	thm
corollary	cor
claim	clm
assumption	asm
example	exm
exercise	exr
conjecture	cnj
hypothesis	hyp
remark	rmk

$$\begin{array}{rl}a& =b\\ & =c\end{array}$$