## Covariance question

1. The problem statement, all variables and given/known data
Let the random variables X and Y have the joint p.m.f.:

f(x,y) = (x+y)/32 x=1,2, y=1,2,3,4.

find the means $$\mu$$x and $$\mu$$y, the variances $$\sigma$$2x and $$\sigma$$2y, and the correlation coefficient $$\rho$$.

2. Relevant equations
$$\rho$$=(COV(X,Y))/$$\sigma$$x$$\sigma$$y

3. The attempt at a solution
I was able to find both $$\mu$$'s:
$$\mu$$x= (25/16)
$$\mu$$y= (45/16)

and both variances:
$$\sigma$$x=(63/256)
$$\sigma$$y=(295/256)

But I cant seem to find how to get the covariance...I tried just using the 1 and 2 values for x and y, but it hasn't worked. I think I'm getting confused because there are more y values than x values. Any help would be much appreciated!

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 Tags correlation, covariance, expected value, probability, statistics