Finished the notes

2026-01-22 10:53:10 -05:00
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  </introduction>
  <subsection xml:id="subsec-hw1-review">
    <title>HW 1 Q5</title>
    <p>
      Write <m>F</m> for the event that there's a fire and <m>S</m> for the event that there's visible smoke.
      Then the information we're given can be interpreted as:
      <md>
        <mrow> \Pr(F) \amp = 0.01 </mrow>
        <mrow> \Pr(S) \amp = 0.1 </mrow>
        <mrow> \Pr(S\mid F) \amp = 0.9 </mrow>
      </md>
      In this case, we can use the simpler version of Bayes' Theorem:
      <md>
        <mrow> \Pr(F \mid S) = \frac{\Pr(S \mid F)\Pr(F)}{\Pr(S)} = \dotsb </mrow>
      </md>
      Unlike our usual diagnostic testing examples, we do have access to the denominator probability here.
    </p>
  </subsection>
  <subsection xml:id="subsec-Discrete-Random-Variables">
    <title>Sec 2.1: Random Variables</title>