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\title{
Exam for Probability \& Statistics (6PAS1) \\ winter semester 2025/2026
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\section*{Questions set no. 1}

\bigskip

\textbf{1.} 
Define expectation and variance of a random variable. Write and prove an 
alternative formula for variance which is mostly used on practice (easier for 
computations).


\bigskip


\textbf{2.}
Prove the memoryless property of the geometric distribution, i.e., 
$P (X > n + k \>|\> X > k) = P (X > n)$ for any $n$ and $k$.



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