\form#0:\[ x_{i+1}\leftarrow(ax_{i} + c) \bmod m \] \form#1:$1$ \form#2:\[ x_{i}\leftarrow(x_{i - s} - x_{i - r} - carry_{i-1}) \bmod m \] \form#3:$r$ \form#4:$(m^r - m^s - 1)$ \form#5:\[ p(x|\mu,\sigma) = \frac{1}{\sigma \sqrt{2 \pi}} e^{- \frac{{x - \mu}^ {2}}{2 \sigma ^ {2}} } \] \form#6:\[ p(x|m,s) = \frac{1}{sx\sqrt{2\pi}} \exp{-\frac{(\ln{x} - m)^2}{2s^2}} \] \form#7:\[ p(x|\alpha,\beta) = \frac{1}{\beta\Gamma(\alpha)} (x/\beta)^{\alpha - 1} e^{-x/\beta} \] \form#8:$p(x|n) = \frac{x^{(n/2) - 1}e^{-x/2}}{\Gamma(n/2) 2^{n/2}}$ \form#9:$p(x|a,b) = (\pi b (1 + (\frac{x-a}{b})^2))^{-1}$ \form#10:\[ p(x|m,n) = \frac{\Gamma((m+n)/2)}{\Gamma(m/2)\Gamma(n/2)} (\frac{m}{n})^{m/2} x^{(m/2)-1} (1 + \frac{mx}{n})^{-(m+n)/2} \] \form#11:\[ p(x|n) = \frac{1}{\sqrt(n\pi)} \frac{\Gamma((n+1)/2)}{\Gamma(n/2)} (1 + \frac{x^2}{n}) ^{-(n+1)/2} \] \form#12:$p$ \form#13:$(1 - p)$ \form#14:$p(i|t,p) = \binom{t}{i} p^i (1 - p)^{t - i}$ \form#15:$t$ \form#16:$p(i|p) = p(1 - p)^{i}$ \form#17:$p(i) = \binom{n}{i} p^i (1 - p)^{t - i}$ \form#18:$p(i|\mu) = \frac{\mu^i}{i!} e^{-\mu}$ \form#19:$\mu$ \form#20:$p(x|\lambda) = \lambda e^{-\lambda x}$ \form#21:$\frac{1}{\lambda}$ \form#22:$\frac{\ln 2}{\lambda}$ \form#23:$zero$ \form#24:$[0, \infty]$ \form#25:\[ p(x|\alpha,\beta) = \frac{\alpha}{\beta} (\frac{x}{\beta})^{\alpha-1} \exp{(-(\frac{x}{\beta})^\alpha)} \] \form#26:\[ p(x|a,b) = \frac{1}{b} \exp( \frac{a-x}{b} - \exp(\frac{a-x}{b})) \] \form#27:$x_0$ \form#28:$ m_{lcg} = 2147483563, a_{lcg} = 40014, c_{lcg} = 0, and lcg(0) = value $ \form#29:$ x_{-r} \dots x_{-1} $ \form#30:$ lcg(1) \bmod m \dots lcg(r) \bmod m $ \form#31:$ x_{-1} = 0 $ \form#32:$mean$ \form#33:$\alpha$ \form#34:$\beta$ \form#35:$[0, 1]$ \form#36:$k$ \form#37:$\lambda$ \form#38:$a$ \form#39:$b$ \form#40:$[min, max]$ \form#41:$\sqrt{\mathrm{end} - \mathrm{begin}}$ \form#42:$1/(\mathrm{oversampling} \cdot \mathrm{num\_parts})$