xbeta
Sandbox

Feel free to test things out by adding to the bottom. This page will be periodically cleaned up so don’t worry about messing anything up.

Tests

Examples

(1) e x 2dx=π2\int_{-\infty}^\infty e^{-x^2} \mathrm{d}x = \frac{\sqrt{\pi}}{2}
Pr(yx)=Pr(yx,v)p(vx)dv\Pr(y \vert x) = \int \Pr(y \vert x, v) p(v \vert x) dv
Ωψ+σ tψ=0\vec{\Omega} \cdot \vec{\nabla} \psi + \sigma_t \psi = 0
(2)β^=(X TX) 1X TY\hat{\mathbf\beta} = (\mathbf X^T\mathbf X)^{-1} \mathbf X^T\mathbf Y

Cases

(3)r a+1={0 with prob.exp(θr a) max{δr a,z} with prob.1exp(θr a) r_{a+1} = \begin{cases} 0 & \text{with prob.}\quad \exp(-\theta r_a) \\ \max \lbrace \delta r_a, z \rbrace & \text{with prob.}\quad 1 - \exp(-\theta r_a) \\ \end{cases}

Stretchy Brackets

q a(z)=σ a 1exp[γ+zσ a]q_a(z) = \sigma_a^{-1} \exp\left[-\frac{\gamma + z}{\sigma_a}\right]

Underset test

Γ 0M×My iM×1+B 0M×Kx iK×1=ε iM×1\underset{M \times M}{\Gamma_0} \underset{M \times 1}{y_i} + \underset{M \times K}{B_0} \underset{K \times 1}{x_i} = \underset{M \times 1}{\varepsilon_i}

Astral plane characters

𝔸 (𝔸)

Display mode test

Note that all display mode equations must be on separate lines. This does not render: [ y = mx + b ]

But this does:

(4)y=mx+by = mx + b

Similarly for dollar signs:

y=mx+by = mx + b

Fraktur and BlackBoard

𝔄𝔅ℭ𝔇𝔈𝔉𝔊ℌℑ𝔍𝔎𝔏𝔐𝔑𝔒𝔓𝔔ℜ𝔖𝔗𝔘𝔙𝔚𝔛𝔜ℨ

𝔸𝔹ℂ𝔻𝔼𝔽𝔾ℍ𝕀𝕁𝕂𝕃𝕄ℕ𝕆ℙℚℝ𝕊𝕋𝕌𝕍𝕎𝕏𝕐ℤ

φ:GG;ker(φ)={gG:φ(g)=e G}\varphi : G \to G'; \qquad \ker(\varphi) = \{ g \in G : \varphi (g) = e_{G'} \}

text text text

f(n)={n/2 ifnis even (n+1)/2 ifnis odd f(n) = \begin{cases} n/2 & \qquad\text{if}\;n\;\text{is even} \\ -(n+1)/2 & \qquad\text{if}\;n\;\text{is odd} \\ \end{cases}

text text text

Theorem

text text text

a Aba\le_A b

text text text

Theorem 1