Fix typos
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Lints / typos (push) Failing after 17s

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2025-01-19 20:24:51 -08:00
parent cb2a1d99dd
commit 5f8c54650f
30 changed files with 105 additions and 49 deletions

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@ -46,17 +46,17 @@ a \textit{random variable} is a function from $\Omega$ to a specified output set
For example, given the three-coin-toss sample space
$\Omega = \{
\texttt{TTT},~ \texttt{TTH},~ \texttt{THT},~
\texttt{THH},~ \texttt{HTT},~ \texttt{HTH},~
\texttt{HHT},~ \texttt{HHH}
\texttt{TTT},~ \texttt{TTH},~ \texttt{THT},~ % spell:disable-line
\texttt{THH},~ \texttt{HTT},~ \texttt{HTH},~ % spell:disable-line
\texttt{HHT},~ \texttt{HHH} % spell:disable-line
\}$,
We can define a random variable $\mathcal{H}$ as \say{the number of heads in a throw of three coins}. \par
As a function, $\mathcal{H}$ maps values in $\Omega$ to values in $\mathbb{Z}^+_0$ and is defined as:
\begin{itemize}
\item $\mathcal{H}(\texttt{TTT}) = 0$
\item $\mathcal{H}(\texttt{TTH}) = 1$
\item $\mathcal{H}(\texttt{THT}) = 1$
\item $\mathcal{H}(\texttt{THH}) = 2$
\item $\mathcal{H}(\texttt{TTT}) = 0$ % spell:disable-line
\item $\mathcal{H}(\texttt{TTH}) = 1$ % spell:disable-line
\item $\mathcal{H}(\texttt{THT}) = 1$ % spell:disable-line
\item $\mathcal{H}(\texttt{THH}) = 2$ % spell:disable-line
\item ...and so on.
\end{itemize}
@ -70,7 +70,7 @@ the set of outcomes that produce that value. \par
\vspace{2mm}
For example, if we wanted to compute $\mathcal{P}(\mathcal{H} = 2)$, we would find
$\mathcal{P}\bigl(\{\texttt{THH}, \texttt{HTH}, \texttt{HHT}\}\bigr)$.
$\mathcal{P}\bigl(\{\texttt{THH}, \texttt{HTH}, \texttt{HHT}\}\bigr)$. % spell:disable-line
\problem{}

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@ -191,7 +191,7 @@ what is the probability that we select the best candidate? \par
Call this probability $\phi_n(k)$.
\begin{solution}
Using \ref{seca} and \ref{secb}, this is straightfoward:
Using \ref{seca} and \ref{secb}, this is straightforward:
\[
\phi_n(k)
= \sum_{x = k}^{n}\left( \frac{1}{n} \times \frac{k-1}{x-1} \right)