okay I want to find the constant c from the equation ${p_{X,Y}(j,k)= c(j+k)}$ where ${j,k=1,2,3}$ for some constant c.
The answer is 1/36. I get that by summarising j and k from 1 to 3 it should equal 1 (sum of all probabilities = 1). But I get c as 1/12. Why are the two variables multiplied? I thougt that the summation should be set up as written below. Obviously I'm wrong(?)
${c* \sum\limits_{j=1}^3\sum\limits_{k=1}^3 (j+k) = 1}$
Any thoughts? Thanks on beforehand
You are right. $c*\sum_{j=1}^{3}\sum_{k=1}^{3}(j + k) = 1$. Though:
$$\sum_{j=1}^{3}\sum_{k=1}^{3}(j + k) = \sum_{j=1}^{3}(j + 1 + j + 2 + j + 3) = \sum_{j=1}^{3}(3j + 6) = 3(1) + 6 + 3(2) + 6 + 3(3) + 6 = 36$$