diff --git a/doc/pub/Statistics/html/._Statistics-bs015.html b/doc/pub/Statistics/html/._Statistics-bs015.html index db2425a82..f6483ad2a 100644 --- a/doc/pub/Statistics/html/._Statistics-bs015.html +++ b/doc/pub/Statistics/html/._Statistics-bs015.html @@ -411,8 +411,8 @@ while \( P(x) \) is the cumulative probability. Domain \( \left\{x_1, x_2, x_3, \dots, x_N\right\} \) \( [a,b] \) Probability \( p(x_i) \) \( p(x)dx \) Cumulative \( P_i=\sum_{l=1}^ip(x_l) \) \( P(x)=\int_a^xp(t)dt \) - Positivity $ 0 \le p(x_i) \le 1$ $ p(x) \ge 0$ - Positivity $ 0 \le P_i \le 1$ $ 0 \le P(x) \le 1$ + Positivity \( 0 \le p(x_i) \le 1 \) \( p(x) \ge 0 \) + Positivity \( 0 \le P_i \le 1 \) \( 0 \le P(x) \le 1 \) Monotonic \( P_i \ge P_j \) if \( x_i \ge x_j \) \( P(x_i) \ge P(x_j) \) if \( x_i \ge x_j \) Normalization \( P_N=1 \) \( P(b)=1 \) diff --git a/doc/pub/Statistics/html/Statistics-reveal.html b/doc/pub/Statistics/html/Statistics-reveal.html index c80275c6a..9faf2ca63 100644 --- a/doc/pub/Statistics/html/Statistics-reveal.html +++ b/doc/pub/Statistics/html/Statistics-reveal.html @@ -616,8 +616,8 @@ while \( P(x) \) is the cumulative probability. Domain \( \left\{x_1, x_2, x_3, \dots, x_N\right\} \) \( [a,b] \) Probability \( p(x_i) \) \( p(x)dx \) Cumulative \( P_i=\sum_{l=1}^ip(x_l) \) \( P(x)=\int_a^xp(t)dt \) - Positivity $ 0 \le p(x_i) \le 1$ $ p(x) \ge 0$ - Positivity $ 0 \le P_i \le 1$ $ 0 \le P(x) \le 1$ + Positivity \( 0 \le p(x_i) \le 1 \) \( p(x) \ge 0 \) + Positivity \( 0 \le P_i \le 1 \) \( 0 \le P(x) \le 1 \) Monotonic \( P_i \ge P_j \) if \( x_i \ge x_j \) \( P(x_i) \ge P(x_j) \) if \( x_i \ge x_j \) Normalization \( P_N=1 \) \( P(b)=1 \) diff --git a/doc/pub/Statistics/html/Statistics-solarized.html b/doc/pub/Statistics/html/Statistics-solarized.html index 4a9e98699..2f6f54cc5 100644 --- a/doc/pub/Statistics/html/Statistics-solarized.html +++ b/doc/pub/Statistics/html/Statistics-solarized.html @@ -748,8 +748,8 @@ while \( P(x) \) is the cumulative probability. Domain \( \left\{x_1, x_2, x_3, \dots, x_N\right\} \) \( [a,b] \) Probability \( p(x_i) \) \( p(x)dx \) Cumulative \( P_i=\sum_{l=1}^ip(x_l) \) \( P(x)=\int_a^xp(t)dt \) - Positivity $ 0 \le p(x_i) \le 1$ $ p(x) \ge 0$ - Positivity $ 0 \le P_i \le 1$ $ 0 \le P(x) \le 1$ + Positivity \( 0 \le p(x_i) \le 1 \) \( p(x) \ge 0 \) + Positivity \( 0 \le P_i \le 1 \) \( 0 \le P(x) \le 1 \) Monotonic \( P_i \ge P_j \) if \( x_i \ge x_j \) \( P(x_i) \ge P(x_j) \) if \( x_i \ge x_j \) Normalization \( P_N=1 \) \( P(b)=1 \) diff --git a/doc/pub/Statistics/html/Statistics.html b/doc/pub/Statistics/html/Statistics.html index 17bb69ebf..69ed6b58c 100644 --- a/doc/pub/Statistics/html/Statistics.html +++ b/doc/pub/Statistics/html/Statistics.html @@ -753,8 +753,8 @@ while \( P(x) \) is the cumulative probability. Domain \( \left\{x_1, x_2, x_3, \dots, x_N\right\} \) \( [a,b] \) Probability \( p(x_i) \) \( p(x)dx \) Cumulative \( P_i=\sum_{l=1}^ip(x_l) \) \( P(x)=\int_a^xp(t)dt \) - Positivity $ 0 \le p(x_i) \le 1$ $ p(x) \ge 0$ - Positivity $ 0 \le P_i \le 1$ $ 0 \le P(x) \le 1$ + Positivity \( 0 \le p(x_i) \le 1 \) \( p(x) \ge 0 \) + Positivity \( 0 \le P_i \le 1 \) \( 0 \le P(x) \le 1 \) Monotonic \( P_i \ge P_j \) if \( x_i \ge x_j \) \( P(x_i) \ge P(x_j) \) if \( x_i \ge x_j \) Normalization \( P_N=1 \) \( P(b)=1 \) diff --git a/doc/pub/Statistics/ipynb b/doc/pub/Statistics/ipynb index fb68379bd..6a461cee4 100644 Binary files a/doc/pub/Statistics/ipynb and b/doc/pub/Statistics/ipynb differ diff --git a/doc/pub/Statistics/pdf/Statistics-beamer-handouts2x3.pdf b/doc/pub/Statistics/pdf/Statistics-beamer-handouts2x3.pdf index 6c17c007b..c12549efe 100644 Binary files a/doc/pub/Statistics/pdf/Statistics-beamer-handouts2x3.pdf and b/doc/pub/Statistics/pdf/Statistics-beamer-handouts2x3.pdf differ diff --git a/doc/pub/Statistics/pdf/Statistics-beamer.pdf b/doc/pub/Statistics/pdf/Statistics-beamer.pdf index 896e1f2ea..bd16717a3 100644 Binary files a/doc/pub/Statistics/pdf/Statistics-beamer.pdf and b/doc/pub/Statistics/pdf/Statistics-beamer.pdf differ diff --git a/doc/pub/Statistics/pdf/Statistics-minted.pdf b/doc/pub/Statistics/pdf/Statistics-minted.pdf index 346e7bb98..24344c9bd 100644 Binary files a/doc/pub/Statistics/pdf/Statistics-minted.pdf and b/doc/pub/Statistics/pdf/Statistics-minted.pdf differ diff --git a/doc/src/Statistics/Statistics.do.txt b/doc/src/Statistics/Statistics.do.txt index 1d4b9aa3e..bd9a121bc 100644 --- a/doc/src/Statistics/Statistics.do.txt +++ b/doc/src/Statistics/Statistics.do.txt @@ -332,8 +332,8 @@ while $P(x)$ is the cumulative probability. | Domain | $\left\{x_1, x_2, x_3, \dots, x_N\right\}$ | $[a,b]$ | | Probability | $p(x_i)$ | $p(x)dx$ | | Cumulative | $P_i=\sum_{l=1}^ip(x_l)$ | $P(x)=\int_a^xp(t)dt$ | -| Positivity | $ 0 \le p(x_i) \le 1$ | $ p(x) \ge 0$ | -| Positivity | $ 0 \le P_i \le 1$ | $ 0 \le P(x) \le 1$ | +| Positivity | $0 \le p(x_i) \le 1$ | $p(x) \ge 0$ | +| Positivity | $0 \le P_i \le 1$ | $0 \le P(x) \le 1$ | | Monotonic | $P_i \ge P_j$ if $x_i \ge x_j$ | $P(x_i) \ge P(x_j)$ if $x_i \ge x_j$ | | Normalization | $P_N=1$ | $P(b)=1$ | |--------------------------------------------------------------------------------------------------------------------------------------|