Covariance

         

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

p(X,Y)X=0X=1X=2Y=00.10.10.2Y=10.20.20Y=200.10.1 \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 XX and Y,Y, which of the following is the same as Cov(X,Y)? \text{Cov}(X,Y)?

If the joint probability density function of continuous random variables X X and Y Y is f(x,y)=16(8x+4y) f(x,y) = \frac{1}{6} \left( 8 x + 4 y \right) with 0x1 and 0y1, 0 \le x \le 1 \text{ and } 0 \le y \le 1, what is the covariance between X X and Y? Y?

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

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

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