[rand] Use modern spelling of \frac and \binom to remove LaTeX warning.

Author: zygoloid

source/numerics.tex

@@ -4527,7 +4527,7 @@
 \indextext{\idxcode{binomial_distribution}!discrete probability function}
 \[%
  P(i\,|\,t,p)
-      = {t \choose i} \cdot p^i \cdot (1-p)^{t-i}
+      = \binom{t}{i} \cdot p^i \cdot (1-p)^{t-i}
 \; \mbox{.}
 \]
 
@@ -4689,7 +4689,7 @@
 \indextext{\idxcode{negative_binomial_distribution}!discrete probability function}
 \[%
  P(i\,|\,k,p)
-      = {k+i-1 \choose i} \cdot p^k \cdot (1-p)^i
+      = \binom{k+i-1}{i} \cdot p^k \cdot (1-p)^i
 \; \mbox{.}
 \]
 
@@ -4947,9 +4947,7 @@
 \indextext{\idxcode{gamma_distribution}!probability density function}
 \[%
  p(x\,|\,\alpha,\beta)
-      = {     e^{-x/\beta}
-        \over {\beta^{\alpha} \cdot \Gamma(\alpha)}
-        }
+      = \frac{e^{-x/\beta}}{\beta^{\alpha} \cdot \Gamma(\alpha)}
         \, \cdot \, x^{\, \alpha-1}
 \; \mbox{.}
 \]
@@ -5237,7 +5235,7 @@
 \indextext{\idxcode{normal_distribution}!probability density function}
 \[%
  p(x\,|\,\mu,\sigma)
-      = {1 \over \sigma \sqrt{2\pi}}
+      = \frac{1}{\sigma \sqrt{2\pi}}
         \cdot
         % e^{-(x-\mu)^2 / (2\sigma^2)}
         \exp{\left(- \, \frac{(x - \mu)^2}
@@ -5969,7 +5967,7 @@
 the remaining $n$ distribution parameters are calculated as:
 \[%
  \rho_k = \;
-   {w_k \over {S \cdot (b_{k+1}-b_k)}}
+   \frac{w_k}{S \cdot (b_{k+1}-b_k)}
    \; \mbox{ for } k = 0, \ldots, n\!-\!1,
 \]
 in which the values $w_k$,
@@ -6175,8 +6173,8 @@
 \indextext{\idxcode{piecewise_linear_distribution}!probability density function}
 \[%
  p(x\,|\,b_0,\ldots,b_n,\;\rho_0,\ldots,\rho_n)
-      = \rho_i     \cdot {{b_{i+1} - x} \over {b_{i+1} - b_i}}
-      + \rho_{i+1} \cdot {{x - b_i} \over {b_{i+1} - b_i}}
+      = \rho_i     \cdot {\frac{b_{i+1} - x}{b_{i+1} - b_i}}
+      + \rho_{i+1} \cdot {\frac{x - b_i}{b_{i+1} - b_i}}
 \; \mbox{,}
 \mbox{ for } b_i \le x < b_{i+1}
 \; \mbox{.}