How do I calculate the problem, $σ_{XY}$ ?
Given the probability distribution calculate $σ_{XY}$
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probability
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1Any try? What is the definition of $\sigma_{XY}$? – 2017-02-12
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0@zoli idk, it just showed up on my online homework and teacher never covered it. – 2017-02-12
1 Answers
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Hint: $\sigma_{XY}$ is the covariance. $$\begin{align}\sigma_{XY} ~ & = ~ \sum_{(x,y)}(x-\mathsf{E}X)(y-\mathsf{E}Y)P(x,y)\\[1ex] & =~ \sum_{(x,y)} xy\,P(x,y) ~-~\mathsf E X\cdot\mathsf EY\end{align}$$ Just substitute all $x$, $y$, and $P(x,y)$ values given in the table (as well as $\mathsf{E}X$ and $\mathsf{E}Y$ given in a.) in the sum. The sum will have $4$ terms.