Some issues concerning joint random variables Let the joint random variable $P[x;y]$ be
$P[x;y] = c[2x^2 + y^2], x=-1;0;1, y=1;2;3;4$
$=0$   $elsewhere$
So I had to find the value of $c$ that makes $P[x;y]$ a joint discrete random variable.
I think I did that right. I just add up all the probabilities where $x = -1;0;1$ and $y = 1;2;3;4$ and made it equal to 1. Then I solved for $c$ and got $c=\frac{1}{106}$. Please check this for me if you think I've done something wrong.
Now they asked to calculate the $E[y]$ and the next question asked if $x$ and $y$ are independent.
So. I was a bit confused with the whole $P[x;y]$ and how to split it up into $P[x]$ and $P[y]$ (if that's possible) and then how to work out the $E[y]$.

I have worked out the problem for you and I hope it helps to check with your answer.  I have done it in EXCEL what other responders have alluded to.  To verify your answer.
