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{\Large \textbf{Sample Questions: Censoring and Likelihood}}%\footnote{}
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STA312 Spring 2019. Copyright information is at the end of the last page.
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The Pareto density is
{ \large
$f(t|\theta) = \left\{ \begin{array}{ll} % ll means left left
   \frac{\theta}{t^{\theta+1}} & \mbox{for $ t \geq 1$}  \\
   0     & \mbox{for } t<1 
   \end{array}  \right. $. % 
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\item Let $(T_1,\delta_1), \ldots, (T_n,\delta_n)$ be a random sample from a Pareto distribution with right censoring. Find the maximum likelihood estimate of $\theta$.  

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\item Find the standard error of $\widehat{\theta}$. \vspace{100mm}

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This assignment was prepared by  \href{http://www.utstat.toronto.edu/~brunner}{Jerry Brunner},
Department of Mathematical and Computational Sciences, University of Toronto. It is licensed under a 
\href{http://creativecommons.org/licenses/by-sa/3.0/deed.en_US}
     {Creative Commons Attribution - ShareAlike 3.0 Unported License}. Use any part of it as you like and share the result freely. The \LaTeX~source code is available from the course website: 
     
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\href{http://www.utstat.toronto.edu/~brunner/oldclass/312s19} {\small\texttt{http://www.utstat.toronto.edu/$^\sim$brunner/oldclass/312s19}}
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