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\begin{document}
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Name \underline{\hspace{60mm}} \\ 
$\,$ \\
Student Number \underline{\hspace{60mm}}
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{\Large \textbf{STA 431 Quiz 3}}\\
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\noindent
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\begin{enumerate} 

\item (5 points) Independently for $i=1, \ldots, n$, let $y_i = \beta x_i + \epsilon_i$, where $x_i \sim N(\mu_x,\sigma^2_x)$, $\epsilon_i \sim N(0,\sigma^2_\epsilon)$, and  $x_i$ and $\epsilon_i$ are independent. Let 
$\widehat{\beta}_n = \frac{\sum_{i=1}^n x_i y_i}{\sum_{i=1}^n x_i^2}$. Is $\widehat{\beta}_n$ a consistent estimator of $\beta$? Answer Yes or No and prove it.


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\item (5 points) \label{R} In Question 16 of this week's assignment, you estimated the parameters of the ``mystery" distribution by maximum likelihood. In the space below, write the maximum likelihood estimate of $\mu$. The answer is a number from your printout. On your printout, circle the number and write ``Question~\ref{R}" beside it. \textbf{Do not answer this question if you do not have a printout.}

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\textbf{Please turn in your printout, showing your \emph{complete} R input and output, with the quiz paper. Make sure your name and student number appear on the printout.}
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