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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.

# Covariance

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 $\text{Cov}(X,Y)?$

If the joint probability density function of continuous random variables $$X$$ and $$Y$$ is $f(x,y) = \frac{1}{6} \left( 8 x + 4 y \right)$ with $$0 \le x \le 1 \text{ and } 0 \le y \le 1,$$ what is the covariance between $$X$$ and $$Y?$$

If $$X$$ and $$Y$$ are independent random variables where $$E[X]=10$$ and $$E[Y]=8,$$ what is $$E[XY]?$$

If the probability distributions of continuous random variables $$X$$ and $$Y$$ are independent of each other, which of the following is equal to $$\text{Cov}(X,Y)?$$

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