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a_{ik} = \frac{L_{ik} \sqrt{\lambda_k}}{\sqrt{L_{1k}^2 + L_{2k}^2 + \dots + L_{mk}^2}}

\begin{cases} (1 - \lambda)L_{11} + r_{12}L_{21} + \dots + r_{1m}L_{m1} = 0 \\ r_{21}L_{11} + (1 - \lambda)L_{21} + \dots + r_{2m}L_{m1} = 0 \\ \dots \\ r_{m1}L_{11} + r_{m2}L_{21} + \dots + (1 - \lambda)L_{m1} = 0 \end{cases}

\sigma_x = \sqrt{\sum_{i=1}^{n} (x_i - \bar{x})^2 \frac{m_i}{N}}

C = \frac{1}{\int_a^b dx} = \left. \frac{1}{x} \right|_a^b = \frac{1}{b - a}

F(x) = \frac{1}{\sigma \sqrt{2\pi}} \int_{-\infty}^{x} e^{-\frac{(z-a)^2}{2\sigma^2}} dz

\begin{vmatrix} (1 - \lambda) & r_{12} & r_{13} & \dots & r_{1m} \\ r_{21} & (1 - \lambda) & r_{23} & \dots & r_{2m} \\ \dots & \dots & \dots & \dots & \dots \\ r_{m1} & r_{m2} & r_{m3} & \dots & (1 - \lambda) \end{vmatrix} = 0

M[X] = a = \int_{-\infty}^{+\infty} x f(x) dx

D[\varphi(x)] = \int_{-\infty}^{+\infty} \varphi^2(x) f(x) dx - [M \varphi(x)]^2

f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x-a)^2}{2\sigma^2}}

P(|X| < \delta) = 2\Phi\left(\frac{\delta}{\sigma}\right)
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