Add standard normal PDF.

docs/stat_dist.html

@@ -421,13 +421,16 @@ <h1 class="title toc-ignore">Statistical distributions</h1>
 <ul>
 <li><span class="math inline">\(E(X) = \mu\)</span></li>
 <li><span class="math inline">\(Var(X) = \sigma^2\)</span></li>
-<li>with <span class="math inline">\(\mu = 0\)</span> and <span class="math inline">\(\sigma = 1\)</span>, it’s called a standard
-normal</li>
 <li>1, 2, 3, standard deviations contain 68% 95% 99% of the density</li>
 <li>the transformation <span class="math inline">\(Z = \frac{X -
-\mu}{\sigma}\)</span> has <span class="math inline">\(\mu = 0, \sigma =
-1\)</span></li>
+\mu}{\sigma}\)</span> gives <span class="math inline">\(\mu = 0\)</span>
+and <span class="math inline">\(\sigma = 1\)</span></li>
+<li>with <span class="math inline">\(\mu = 0\)</span> and <span class="math inline">\(\sigma = 1\)</span>, it’s called a standard
+normal</li>
 </ul>
+<p><span class="math display">\[
+P(Z = x) = f(x) = \frac{1}{\sqrt{2 \pi}} e ^{- \frac{x^2}{2}},
+\]</span></p>
 <hr />
 <ul>
 <li><a href="./stat_inf.html">next: Statistical inference</a></li>

rmd_sources/stat_inf/stat_dist.Rmd

@@ -77,9 +77,13 @@ Properties:
 
 - $E(X) = \mu$
 - $Var(X) = \sigma^2$
-- with $\mu = 0$ and $\sigma = 1$, it's called a standard normal
 - 1, 2, 3, standard deviations contain 68% 95% 99% of the density
-- the transformation $Z = \frac{X - \mu}{\sigma}$ has $\mu = 0, \sigma = 1$
+- the transformation $Z = \frac{X - \mu}{\sigma}$ gives $\mu = 0$ and $\sigma = 1$
+- with $\mu = 0$ and $\sigma = 1$, it's called a standard normal
+
+$$
+P(Z = x) = f(x) = \frac{1}{\sqrt{2 \pi}} e ^{- \frac{x^2}{2}},
+$$
 
 ***