the probability function of a random vector

Question

We've got a random vector with the following probability funtion:
P(X=i,Y=j)=k(i+j) where (i,j) into the image of (X,Y) which is {(l,m) / 1<=l<=n and 1<=m<=q}
How can I calculate the value of k?

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I know that to calculate k I have to calculate the summatory of the values of x and y of k(i+j). But in this case I don't know how to do it because I don't know how many terms I have to sum. Is right that x goes from 1 to n and m goes from 1 to q? Anyway, I don't know how to do it in this case...

Answer 1

Hint:

$$\sum_{l=1}^{n}\sum_{m=1}^qP(X=l,Y=m)=1$$