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 <h1 id="Notes:-Review-of-Probability">Notes: Review of Probability<a class="anchor-link" href="#Notes:-Review-of-Probability">&#182;</a></h1><p>Containing:</p>
 <ul>
-<li>a review of the most revelant tools of mathemetical probability</li>
+<li>a review of the most relevant tools of mathematical probability</li>
 <li>some common probability distributions to be familiar with</li>
 </ul>
 
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-<p>For completeness, one can also define the straighforward generalization of the CDF,</p>
+<p>For completeness, one can also define the straightforward generalization of the CDF,</p>
 <p>$F(x',y') = P(x \leq x', y \leq y')$.</p>
 <p>However the inverse (quantile) function is now multivalued, which can make them less useful, at least for some purposes. We probably won't see either the CDF or quantile function used in the multivariate case.</p>
 
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-<h2 id="Probability-calculus">Probability calculus<a class="anchor-link" href="#Probability-calculus">&#182;</a></h2><p>The section above outlines the basic operations we can perform on probabilities and probability densitites, namely marginalization and conditioning. Rather than diving into the formalities of probability as a branch of mathematics, we hope that learning by example in the later notes will be enough. Still, here are a couple of basic rules that will hopefully avoid confusion:</p>
+<h2 id="Probability-calculus">Probability calculus<a class="anchor-link" href="#Probability-calculus">&#182;</a></h2><p>The section above outlines the basic operations we can perform on probabilities and probability densities, namely marginalization and conditioning. Rather than diving into the formalities of probability as a branch of mathematics, we hope that learning by example in the later notes will be enough. Still, here are a couple of basic rules that will hopefully avoid confusion:</p>
 <ol>
 <li>One cannot marginalize over a variable if it appears only to the <em>right</em> of a &quot;|&quot;, because variables that are conditioned on are necessarily fixed as far as the expression they appear in is concerned.</li>
 <li>Pedantically applying the definition of conditional probability and substituting into an equation is <strong>much safer</strong> than trying to intuit when and where &quot;|&quot; can just be dropped in.</li>
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-<h3 id="Poisson-distribution">Poisson distribution<a class="anchor-link" href="#Poisson-distribution">&#182;</a></h3><p>... which describes the number of successes when the number of trials is in principle infinite, and $q$ is correspondingly vanishingly small. It has a single parameter, $\mu$, which corresponds to the product $qn$ when interpretted as a limit of the Binomial distribution. The PMF is</p>
+<h3 id="Poisson-distribution">Poisson distribution<a class="anchor-link" href="#Poisson-distribution">&#182;</a></h3><p>... which describes the number of successes when the number of trials is in principle infinite, and $q$ is correspondingly vanishingly small. It has a single parameter, $\mu$, which corresponds to the product $qn$ when interpreted as a limit of the Binomial distribution. The PMF is</p>
 <p>$P(k|\mu) = \frac{\mu^k e^{-\mu}}{k!}$.</p>
 <p>Like the Binomial distribution, the Poisson distribution is additive. It has the following (probably familiar) properties:</p>
 <ul>