\documentclass{article}
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\usepackage{times}
\usepackage{amsmath}

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\begin{document}
$\frac{(1*1.0+2*2.0+3*3.0+4*4.0+5*5.0+6*6.0+7*7.0+8*8.0+9*9.0)}
             {1+2+3+4+5+6+7+8+9}$
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$1*1.0+2*2.0+3*3.0+4*4.0+5*5.0+6*6.0+7*7.0+8*8.0+9*9.0$
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$\frac{(1*1.0+2*2.0+3*3.0+4*4.0+5*5.0+6*6.0+7*7.0+8*8.0+9*9.0)}{1+2+3+4+5+6+7+8+9}$
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$10 \times\text{\texttt{DBL\_EPSILON}} \times \max(N, M)$
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$[0,1]$
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$\chi^2$
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\[z = B + \frac{A}{2 \pi \sigma_x \sigma_y \sqrt{1-\rho^2}} 
\exp\left({-\frac{1}{2\left(1-\rho^2\right)}
\left(\left(\frac{x - \mu_x}{\sigma_x}\right)^2 
-2\rho\left(\frac{x - \mu_x}{\sigma_x}\right)
\left(\frac{y - \mu_y}{\sigma_y}\right) 
+ \left(\frac{y - \mu_y}{\sigma_y}\right)^2\right)}\right)
\]
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$B$
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$A$
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\begin{eqnarray*}\mathrm{parameters[0]} &=& B \\
\mathrm{parameters[1]} &=& A \\
\mathrm{parameters[2]} &=& \rho \\
\mathrm{parameters[3]} &=& \mu_x \\
\mathrm{parameters[4]} &=& \mu_y \\
\mathrm{parameters[5]} &=& \sigma_x \\
\mathrm{parameters[6]} &=& \sigma_y
\end{eqnarray*}
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$a, b$
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$\theta$
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\begin{eqnarray*}\theta &=& \frac{1}{2} \arctan \left(2 \rho \frac{\sigma_x \sigma_y}
                       {\sigma_x^2 - \sigma_y^2}\right) \\
a &=& \sigma_x \sigma_y \sqrt{2(1-\rho^2) \frac{\cos 2\theta}
                        {\left(\sigma_x^2 + \sigma_y^2\right) \cos 2\theta
                        + \sigma_y^2 - \sigma_x^2}} \\
b &=& \sigma_x \sigma_y \sqrt{2(1-\rho^2) \frac{\cos 2\theta}
                        {\left(\sigma_x^2 + \sigma_y^2\right) \cos 2\theta
                        - \sigma_y^2 + \sigma_x^2}}
\end{eqnarray*}
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$x$
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$-\pi/2$
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$+\pi/2$
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$\rho = 0$
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$\sigma_x \geq \sigma_y$
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\begin{eqnarray*}\theta &=& 0 \\
a &=& \sigma_x \\
b &=& \sigma_y 
\end{eqnarray*}
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$\sigma_x < \sigma_y$
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$y$
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\begin{eqnarray*}\theta &=& \frac{\pi}{2} \\
a &=& \sigma_y \\
b &=& \sigma_x 
\end{eqnarray*}
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\[         \mathrm{G} = \mathrm{J} \mathrm{C} \mathrm{J}^\mathrm{T}
\]
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$(B, A, \rho, \mu_x, \mu_y, \sigma_x, \sigma_y) \rightarrow (\theta, a, b)
$
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$x_{max} = w/2 + k * \sigma,$
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$w$
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$\sigma = w_{FWHM}/(2\sqrt(2\log(2))),$
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$w_{FWHM}$
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$k$
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\end{document}
