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andy
2026-08-01 18:43:12 +00:00
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source/sec-Variance.ptx
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<statement> <statement>
<p> <p>
Suppose we flip a coin <m>n = 100</m> times, and let <m>N</m> count the number of heads. Suppose we flip a coin <m>n = 100</m> times, and let <m>N</m> count the number of heads.
If the coin comes up heads on a flip with probability <m>p = 0.4</m>, what is <m>\Var(N)</m>? What if <m>n = 80</m> and <m>p = 0.6</m>? What if <m>n = 200</m> and <m>p = 0.5</m>? If the coin comes up heads on a flip with probability <m>p = 0.3</m>, what is <m>\Var(N)</m>? What if <m>n = 80</m> and <m>p = 0.6</m>? What if <m>n = 200</m> and <m>p = 0.5</m>?
</p> </p>
</statement> </statement>
<answer>
<p>
When <m>n = 100</m> and <m>p = 0.3</m>, <m>\Var(N) = 21</m>.
When <m>n = 80</m> and <m>p = 0.6</m>, <m>\Var(N) = 19.2</m>.
When <m>n = 200</m> and <m>p = 0.5</m>, <m>\Var(N) = 50</m>.
</p>
</answer>
</exercise> </exercise>
<exercise> <exercise>