Let the joint pdf of $X$ and $Y$ be given by $f(x,y)=c(x^2+y^2)$, for $x=-1,0,1,3$ and $y=-1,2,3$ where $c$ is a constant.

Question

Let the joint pdf of $X$ and $Y$ be given by $f(x,y)=c(x^2+y^2)$, for $x=-1,0,1,3$ and $y=-1,2,3$ where $c$ is a constant.

(a) Find the value of $c$.

(b) Find the conditional distribution table of $X$, given that $Y=2$

(c) Compute $P(X>2-Y)$.

(d) Compute $Cov(X,Y)$.

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For some reason I'm having a lot of trouble with this question... I can't figure out how you can find the value of c at all... Any help/hints would be greatly appreciated. Thanks in advance!