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# Variance

Would you rather get paid $2 for flipping heads, or $6 for rolling a "1"? The expected value is the same ($1)...but the bets are different! Variance and standard deviation add color to probability.

If the joint probability distribution function of \( X \) and \( Y \) is given as follows, what is \( 20 \text{Cov}(X,Y) ? \)

\[ \begin{matrix} p(X,Y) & X=0 & X=1 & X=2 \\ Y=0 & 0.1 & 0.1 & 0.2 \\ Y=1 & 0.2 & 0.2 & 0 \\ Y=2 & 0 & 0.1 & 0.1 \end{matrix} \]

For random variables \(X\) and \(Y,\) which of the following is the same as \[ \text{Cov}(X,Y)? \]

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