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\begin{document}

\title{
Exam for Probability \& Statistics (6PAS1) \\ winter semester 2025/2026
}

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\section*{Questions set no. 3}

\bigskip

\textbf{1.} 
Formulate and prove the inclusion-exclusion princile. Does the same principle
hold for infinite sets?

\bigskip


\textbf{2.}
Compute the correlation between the random variables $X$ and $Y$, if their joint
probability function is given by the following table. Also compute the 
correlation between $X^2$ and $Y^2$.

\begin{center}
$X$
\smallskip
\\
$Y$
\begin{tabular}{|c|c|c|}
\hline
   & 0    & 1    \\ \hline
-1 & 7/30 & 1/10 \\ \hline
0  & 4/30 & 2/10 \\ \hline
1  & 1/30 & 3/10 \\ \hline
\end{tabular}
\end{center}




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