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docs: render equations via math code blocks
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Planeshifter committed Mar 7, 2023
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Expand Up @@ -28,10 +28,14 @@ The [cumulative distribution function][cdf] for an [arcsine][arcsine-distributio

<!-- <equation class="equation" label="eq:arcsine_cdf" align="center" raw="F(x) = \frac{2}{\pi} \arcsin \left( \sqrt{\frac{x-a}{b-a}} \right)" alt="Cumulative distribution function for an arcsine distribution."> -->

<div class="equation" align="center" data-raw-text="F(x) = \frac{2}{\pi} \arcsin \left( \sqrt{\frac{x-a}{b-a}} \right)" data-equation="eq:arcsine_cdf">
```math
F(x) = \frac{2}{\pi} \arcsin \left( \sqrt{\frac{x-a}{b-a}} \right)
```

<!-- <div class="equation" align="center" data-raw-text="F(x) = \frac{2}{\pi} \arcsin \left( \sqrt{\frac{x-a}{b-a}} \right)" data-equation="eq:arcsine_cdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/cdf/docs/img/equation_arcsine_cdf.svg" alt="Cumulative distribution function for an arcsine distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -30,10 +30,14 @@ The [differential entropy][entropy] (in [nats][nats]) for an [arcsine][arcsine-d

<!-- <equation class="equation" label="eq:arcsine_entropy" align="center" raw="h\left( X \right) = \ln {\tfrac{\pi}{4}}" alt="Differential entropy for an arcsine distribution."> -->

<div class="equation" align="center" data-raw-text="h\left( X \right) = \ln {\tfrac{\pi}{4}}" data-equation="eq:arcsine_entropy">
```math
h\left( X \right) = \ln {\tfrac{\pi}{4}}
```

<!-- <div class="equation" align="center" data-raw-text="h\left( X \right) = \ln {\tfrac{\pi}{4}}" data-equation="eq:arcsine_entropy">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/entropy/docs/img/equation_arcsine_entropy.svg" alt="Differential entropy for an arcsine distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -30,10 +30,14 @@ The [excess kurtosis][kurtosis] for an [arcsine][arcsine-distribution] random va

<!-- <equation class="equation" label="eq:arcsine_kurtosis" align="center" raw="\operatorname{Kurt}\left( X \right) = -{\frac {3}{5}}" alt="Excess kurtosis for an arcsine distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = -{\frac {3}{5}}" data-equation="eq:arcsine_kurtosis">
```math
\operatorname{Kurt}\left( X \right) = -{\frac {3}{5}}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = -{\frac {3}{5}}" data-equation="eq:arcsine_kurtosis">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/kurtosis/docs/img/equation_arcsine_kurtosis.svg" alt="Excess kurtosis for an arcsine distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -28,10 +28,14 @@ The [cumulative distribution function][cdf] for an [arcsine][arcsine-distributio

<!-- <equation class="equation" label="eq:arcsine_cdf" align="center" raw="F(x) = \frac{2}{\pi} \arcsin \left( \sqrt{\frac{x-a}{b-a}} \right)" alt="Cumulative distribution function for an arcsine distribution."> -->

<div class="equation" align="center" data-raw-text="F(x) = \frac{2}{\pi} \arcsin \left( \sqrt{\frac{x-a}{b-a}} \right)" data-equation="eq:arcsine_cdf">
```math
F(x) = \frac{2}{\pi} \arcsin \left( \sqrt{\frac{x-a}{b-a}} \right)
```

<!-- <div class="equation" align="center" data-raw-text="F(x) = \frac{2}{\pi} \arcsin \left( \sqrt{\frac{x-a}{b-a}} \right)" data-equation="eq:arcsine_cdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/logcdf/docs/img/equation_arcsine_cdf.svg" alt="Cumulative distribution function for an arcsine distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -28,10 +28,14 @@ The [probability density function][pdf] (PDF) for a [arcsine][arcsine-distributi

<!-- <equation class="equation" label="eq:arcsine_pdf" align="center" raw="f(x;a,b)=\begin{cases} {\frac{1}{\pi {\sqrt{(x-a)(b-x)}}}} & \text{for } x \in [a,b] \\ 0 & \text{otherwise} \end{cases}" alt="Probability density function (PDF) for an distribution."> -->

<div class="equation" align="center" data-raw-text="f(x;a,b)=\begin{cases} {\frac{1}{\pi {\sqrt{(x-a)(b-x)}}}} &amp; \text{for } x \in [a,b] \\ 0 &amp; \text{otherwise} \end{cases}" data-equation="eq:arcsine_pdf">
```math
f(x;a,b)=\begin{cases} {\frac{1}{\pi {\sqrt{(x-a)(b-x)}}}} & \text{for } x \in [a,b] \\ 0 & \text{otherwise} \end{cases}
```

<!-- <div class="equation" align="center" data-raw-text="f(x;a,b)=\begin{cases} {\frac{1}{\pi {\sqrt{(x-a)(b-x)}}}} &amp; \text{for } x \in [a,b] \\ 0 &amp; \text{otherwise} \end{cases}" data-equation="eq:arcsine_pdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/logpdf/docs/img/equation_arcsine_pdf.svg" alt="Probability density function (PDF) for an distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -30,10 +30,14 @@ The [expected value][expected-value] for an [arcsine][arcsine-distribution] rand

<!-- <equation class="equation" label="eq:arcsine_expectation" align="center" raw="\mathbb{E}\left[ X \right] = 0.5 \cdot ( a + b )" alt="Expected value for an arcsine distribution."> -->

<div class="equation" align="center" data-raw-text="\mathbb{E}\left[ X \right] = 0.5 \cdot ( a + b )" data-equation="eq:arcsine_expectation">
```math
\mathbb{E}\left[ X \right] = 0.5 \cdot ( a + b )
```

<!-- <div class="equation" align="center" data-raw-text="\mathbb{E}\left[ X \right] = 0.5 \cdot ( a + b )" data-equation="eq:arcsine_expectation">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/mean/docs/img/equation_arcsine_expectation.svg" alt="Expected value for an arcsine distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -30,10 +30,14 @@ The [median][median] for an [arcsine][arcsine-distribution] random variable is

<!-- <equation class="equation" label="eq:arcsine_median" align="center" raw="\operatorname{Median}\left( X \right) = \frac{1}{2} \cdot ( a + b )" alt="Median for an arcsine distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Median}\left( X \right) = \frac{1}{2} \cdot ( a + b )" data-equation="eq:arcsine_median">
```math
\operatorname{Median}\left( X \right) = \frac{1}{2} \cdot ( a + b )
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{Median}\left( X \right) = \frac{1}{2} \cdot ( a + b )" data-equation="eq:arcsine_median">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/median/docs/img/equation_arcsine_median.svg" alt="Median for an arcsine distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -30,10 +30,14 @@ The [mode][mode] for an [arcsine][arcsine-distribution] random variable with wit

<!-- <equation class="equation" label="eq:arcsine_mode" align="center" raw="\operatorname{mode}\left( X \right) = \{ a, b \}" alt="Mode for an arcsine distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{mode}\left( X \right) = \{ a, b \}" data-equation="eq:arcsine_mode">
```math
\operatorname{mode}\left( X \right) = \{ a, b \}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{mode}\left( X \right) = \{ a, b \}" data-equation="eq:arcsine_mode">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/mode/docs/img/equation_arcsine_mode.svg" alt="Mode for an arcsine distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -28,10 +28,14 @@ The [probability density function][pdf] (PDF) for an [arcsine][arcsine-distribut

<!-- <equation class="equation" label="eq:arcsine_pdf" align="center" raw="f(x;a,b)=\begin{cases} {\frac{1}{\pi {\sqrt{(x-a)(b-x)}}}} & \text{for } x \in [a,b] \\ 0 & \text{otherwise} \end{cases}" alt="Probability density function (PDF) for an arcsine distribution."> -->

<div class="equation" align="center" data-raw-text="f(x;a,b)=\begin{cases} {\frac{1}{\pi {\sqrt{(x-a)(b-x)}}}} &amp; \text{for } x \in [a,b] \\ 0 &amp; \text{otherwise} \end{cases}" data-equation="eq:arcsine_pdf">
```math
f(x;a,b)=\begin{cases} {\frac{1}{\pi {\sqrt{(x-a)(b-x)}}}} & \text{for } x \in [a,b] \\ 0 & \text{otherwise} \end{cases}
```

<!-- <div class="equation" align="center" data-raw-text="f(x;a,b)=\begin{cases} {\frac{1}{\pi {\sqrt{(x-a)(b-x)}}}} &amp; \text{for } x \in [a,b] \\ 0 &amp; \text{otherwise} \end{cases}" data-equation="eq:arcsine_pdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/pdf/docs/img/equation_arcsine_pdf.svg" alt="Probability density function (PDF) for an arcsine distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -28,10 +28,14 @@ The [quantile function][quantile-function] for an [arcsine][arcsine-distribution

<!-- <equation class="equation" label="eq:arcsine_quantile_function" align="center" raw="Q(p) = a + ( b - a ) \sin^2 \left( \tfrac{\pi}{2} p \right)" alt="Quantile function for an arcsine distribution."> -->

<div class="equation" align="center" data-raw-text="Q(p) = a + ( b - a ) \sin^2 \left( \tfrac{\pi}{2} p \right)" data-equation="eq:arcsine_quantile_function">
```math
Q(p) = a + ( b - a ) \sin^2 \left( \tfrac{\pi}{2} p \right)
```

<!-- <div class="equation" align="center" data-raw-text="Q(p) = a + ( b - a ) \sin^2 \left( \tfrac{\pi}{2} p \right)" data-equation="eq:arcsine_quantile_function">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/arcsine/quantile/docs/img/equation_arcsine_quantile_function.svg" alt="Quantile function for an arcsine distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -30,10 +30,14 @@ The [skewness][skewness] for an [arcsine][arcsine-distribution] random variable

<!-- <equation class="equation" label="eq:arcsine_skewness" align="center" raw="\operatorname{skew}\left( X \right) = 0" alt="Skewness for an arcsine distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{skew}\left( X \right) = 0" data-equation="eq:arcsine_skewness">
```math
\operatorname{skew}\left( X \right) = 0
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{skew}\left( X \right) = 0" data-equation="eq:arcsine_skewness">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/skewness/docs/img/equation_arcsine_skewness.svg" alt="Skewness for an arcsine distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -30,10 +30,14 @@ The [standard deviation][stdev] for an [arcsine][arcsine-distribution] random va

<!-- <equation class="equation" label="eq:arcsine_stdev" align="center" raw="\sigma = {\tfrac{1}{\sqrt{8}}}(b-a)" alt="Standard deviation for an arcsine distribution."> -->

<div class="equation" align="center" data-raw-text="\sigma = {\tfrac{1}{\sqrt{8}}}(b-a)" data-equation="eq:arcsine_stdev">
```math
\sigma = {\tfrac{1}{\sqrt{8}}}(b-a)
```

<!-- <div class="equation" align="center" data-raw-text="\sigma = {\tfrac{1}{\sqrt{8}}}(b-a)" data-equation="eq:arcsine_stdev">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/stdev/docs/img/equation_arcsine_stdev.svg" alt="Standard deviation for an arcsine distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -30,10 +30,14 @@ The [variance][variance] for an [arcsine][arcsine-distribution] random variable

<!-- <equation class="equation" label="eq:arcsine_variance" align="center" raw="\operatorname{Var}\left( X \right) = {\tfrac {1}{8}}(b-a)^{2}" alt="Variance for an arcsine distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Var}\left( X \right) = {\tfrac {1}{8}}(b-a)^{2}" data-equation="eq:arcsine_variance">
```math
\operatorname{Var}\left( X \right) = {\tfrac {1}{8}}(b-a)^{2}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{Var}\left( X \right) = {\tfrac {1}{8}}(b-a)^{2}" data-equation="eq:arcsine_variance">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/arcsine/variance/docs/img/equation_arcsine_variance.svg" alt="Variance for an arcsine distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -28,10 +28,14 @@ The [cumulative distribution function][cdf] for a [Bernoulli][bernoulli-distribu

<!-- <equation class="equation" label="eq:bernoulli_cdf" align="center" raw="F(x;p)= \begin{cases} 0 & \text{ for } x < 0 \\ 1-p & \text{ for } 0 \le x < 1 \\ 1 & \text{ for } x \ge 1 \end{cases}" alt="Cumulative distribution function for a Bernoulli distribution."> -->

<div class="equation" align="center" data-raw-text="F(x;p)= \begin{cases} 0 &amp; \text{ for } x &lt; 0 \\ 1-p &amp; \text{ for } 0 \le x &lt; 1 \\ 1 &amp; \text{ for } x \ge 1 \end{cases}" data-equation="eq:bernoulli_cdf">
```math
F(x;p)= \begin{cases} 0 & \text{ for } x < 0 \\ 1-p & \text{ for } 0 \le x < 1 \\ 1 & \text{ for } x \ge 1 \end{cases}
```

<!-- <div class="equation" align="center" data-raw-text="F(x;p)= \begin{cases} 0 &amp; \text{ for } x &lt; 0 \\ 1-p &amp; \text{ for } 0 \le x &lt; 1 \\ 1 &amp; \text{ for } x \ge 1 \end{cases}" data-equation="eq:bernoulli_cdf">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/bernoulli/cdf/docs/img/equation_bernoulli_cdf.svg" alt="Cumulative distribution function for a Bernoulli distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -30,10 +30,14 @@ The [entropy][entropy] (in [nats][nats]) for a [Bernoulli][bernoulli-distributio

<!-- <equation class="equation" label="eq:bernoulli_entropy" align="center" raw="H\left( X \right) = -q \ln( q ) - p \ln( p )" alt="Differential entropy for a bernoulli distribution."> -->

<div class="equation" align="center" data-raw-text="H\left( X \right) = -q \ln( q ) - p \ln( p )" data-equation="eq:bernoulli_entropy">
```math
H\left( X \right) = -q \ln( q ) - p \ln( p )
```

<!-- <div class="equation" align="center" data-raw-text="H\left( X \right) = -q \ln( q ) - p \ln( p )" data-equation="eq:bernoulli_entropy">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/bernoulli/entropy/docs/img/equation_bernoulli_entropy.svg" alt="Differential entropy for a bernoulli distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -30,10 +30,14 @@ The [excess kurtosis][kurtosis] for a [Bernoulli][bernoulli-distribution] random

<!-- <equation class="equation" label="eq:bernoulli_kurtosis" align="center" raw="\operatorname{Kurt}\left( X \right) = \frac{1}{pq} - 6" alt="Excess kurtosis for a Bernoulli distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = \frac{1}{pq} - 6" data-equation="eq:bernoulli_kurtosis">
```math
\operatorname{Kurt}\left( X \right) = \frac{1}{pq} - 6
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{Kurt}\left( X \right) = \frac{1}{pq} - 6" data-equation="eq:bernoulli_kurtosis">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/bernoulli/kurtosis/docs/img/equation_bernoulli_kurtosis.svg" alt="Excess kurtosis for a Bernoulli distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -30,10 +30,14 @@ The [expected value][expected-value] for a [Bernoulli][bernoulli-distribution] r

<!-- <equation class="equation" label="eq:bernoulli_expectation" align="center" raw="\mathbb{E}\left[ X \right] = p" alt="Expected value for a Bernoulli distribution."> -->

<div class="equation" align="center" data-raw-text="\mathbb{E}\left[ X \right] = p" data-equation="eq:bernoulli_expectation">
```math
\mathbb{E}\left[ X \right] = p
```

<!-- <div class="equation" align="center" data-raw-text="\mathbb{E}\left[ X \right] = p" data-equation="eq:bernoulli_expectation">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/bernoulli/mean/docs/img/equation_bernoulli_expectation.svg" alt="Expected value for a Bernoulli distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -30,10 +30,14 @@ The [median][median] for a [Bernoulli][bernoulli-distribution] random variable i

<!-- <equation class="equation" label="eq:bernoulli_median" align="center" raw="\operatorname{Median}\left( X \right) = \begin{cases} 0 & \text{if } p \le 0.5 \\ 1 & \text{if } p > 0.5 \end{cases}" alt="Median for a Bernoulli distribution."> -->

<div class="equation" align="center" data-raw-text="\operatorname{Median}\left( X \right) = \begin{cases} 0 &amp; \text{if } p \le 0.5 \\ 1 &amp; \text{if } p &gt; 0.5 \end{cases}" data-equation="eq:bernoulli_median">
```math
\operatorname{Median}\left( X \right) = \begin{cases} 0 & \text{if } p \le 0.5 \\ 1 & \text{if } p > 0.5 \end{cases}
```

<!-- <div class="equation" align="center" data-raw-text="\operatorname{Median}\left( X \right) = \begin{cases} 0 &amp; \text{if } p \le 0.5 \\ 1 &amp; \text{if } p &gt; 0.5 \end{cases}" data-equation="eq:bernoulli_median">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/bernoulli/median/docs/img/equation_bernoulli_median.svg" alt="Median for a Bernoulli distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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Expand Up @@ -30,10 +30,14 @@ The [moment-generating function][mgf] for a [Bernoulli][bernoulli-distribution]

<!-- <equation class="equation" label="eq:bernoulli_mgf_function" align="center" raw="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = 1-p + p \exp( t )" alt="Moment-generating function (MGF) for a Bernoulli distribution."> -->

<div class="equation" align="center" data-raw-text="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = 1-p + p \exp( t )" data-equation="eq:bernoulli_mgf_function">
```math
M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = 1-p + p \exp( t )
```

<!-- <div class="equation" align="center" data-raw-text="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = 1-p + p \exp( t )" data-equation="eq:bernoulli_mgf_function">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@591cf9d5c3a0cd3c1ceec961e5c49d73a68374cb/lib/node_modules/@stdlib/stats/base/dists/bernoulli/mgf/docs/img/equation_bernoulli_mgf_function.svg" alt="Moment-generating function (MGF) for a Bernoulli distribution.">
<br>
</div>
</div> -->

<!-- </equation> -->

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