\documentclass{jsarticle}
\usepackage{amsmath}
\usepackage{statexv12}
\usepackage{boxedminipage}

\renewcommand*{\ha}{{\alpha/2}}

\begin{document}

$$
\lp \rp \lb \rb
$$

$$
\^{\beta_1}=\^{\beta}_1=b_1
$$

$\H_0: \mu_\ikj=0$ vs. $\H_1: \mu_\ikj \neq 0$
$$
\H_0: \mu_\ikj=0 \text{ vs. } \H_1: \mu_\ikj \neq 0
$$

$\logit \lb p \rb = \log \lb \frac{p}{1-p} \rb$
$$
\logit \lb p \rb = \log \lb \frac{p}{1-p} \rb
$$

$$
\E[z]{Z}=0, \V[z]{Z}=1, \and \P[z]{|Z|>z_\ha}=\alpha
$$

$Z ~ \N{0, 1}, \where \E{Z}=0 \and \V{Z}=1$
\begin{align*}
& Z ~ \N{0, 1}, \where \E{Z}=0 \and \V{Z}=1\\
& \P{|Z|>z_\ha}=\alpha\\
& \pN[z]{0}{1}        \\
& \pN[z]{\mu}{\sd^2}  \\
& \bm{X} ~ \N[p]{\bm{\mu}, \sfsl{\Sigma}}
\end{align*}

$ Z_i \iid \N{0, 1}, \where i=1 ,\., n$
\begin{align*}
& Z_i \iid \N{0, 1}, \where i=1 ,\., n\\
& \chisq = \sum_i Z_i^2 ~ \Chi{n}\\
& \pChi[z]{n}
\end{align*}

$$
\frac{\b{Z}}{\sqrt{\frac{\chisq}{n}}} ~ \tdist{n}
$$

$ X_i, Y_i \iid \N{0, 1}, \where i=1 ,\., n, \\
 \V{X_i, Y_{\~i}}=\sd_\xy=0, \and \~i=1 ,\., n $
\begin{align*}
& \chisq_x = \sum_i X_i^2 ~ \Chi{n} \\
& \chisq_y = \sum_i Y_i^2 ~ \Chi{n} \\
& \frac{\chisq_x}{\chisq_y} ~ \F{n, n}
\end{align*}

\end{document}
