Merge branch 'master' of github.com:chiphuyen/ml-interviews-book

Author: chiphuyen

_book/contents/5.2.1.1-basic-concepts-to-review.html

@@ -1778,7 +1778,7 @@ <h6 id="geometric-random-variable">Geometric random variable</h6>
 <h6 id="beta-random-variable">Beta random variable</h6>
 <p>Beta is my favorite distribution (what do you mean you don&apos;t have a favorite distribution?). It&apos;s a random variable that estimates another random variable.</p>
 <p>Say, we have a coin with an unknown probability of turning heads. Let <script type="math/tex; ">p</script> represent this probability. After <script type="math/tex; ">n + m</script> flips, we get <script type="math/tex; ">n</script> heads and <script type="math/tex; ">m</script> tails. We might want to estimate that <script type="math/tex; ">p = \frac{n}{n+m}</script>. However, this is unreliable, especially if <script type="math/tex; ">n+m</script> is small. We&apos;d like to say something like this: <script type="math/tex; ">p</script> can also be more than, less than, or equal to <script type="math/tex; ">\frac{n}{n+m}</script>, the values further away from <script type="math/tex; ">\frac{n}{n+m}</script> having a smaller probability. And the higher the value of <script type="math/tex; ">n+m</script>, the higher the probability of <script type="math/tex; ">p</script> being <script type="math/tex; ">\frac{n}{n+m}</script>. The beta distribution allows you to do that.</p>
-<p>The beta random variable is represented using two variables: <script type="math/tex; ">\alpha</script> to represent the number of successes and <script type="math/tex; ">\beta</script> to represent the number of failures. The beta distribution can represent beyond coin flips. In fact, <script type="math/tex; ">\alpha</script> and <script type="math/tex; ">\beta</script> can rerepsent continuous value (though they can&apos;t be non-positive).</p>
+<p>The beta random variable is represented using two variables: <script type="math/tex; ">\alpha</script> to represent the number of successes and <script type="math/tex; ">\beta</script> to represent the number of failures. The beta distribution can represent beyond coin flips. In fact, <script type="math/tex; ">\alpha</script> and <script type="math/tex; ">\beta</script> can represent continuous value (though they can&apos;t be non-positive).</p>
 <p><script type="math/tex; mode=display">
  x \sim \text{Beta}(\alpha, \beta) \text{ with } 0 < \alpha, \beta \\
  f(x; \alpha, \beta) = \frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha)\Gamma(\beta)}x^{\alpha-1}(1-x)^{\beta-1} \text{ with } 0 \leq x \leq 1