This builds on Probability Theory

Joint Random Variable

We have a joint random variable (X,Y)(X,Y) and we want to find a pair of values

P(x,y)=∑x,y∈Vx,yP(e)Vx,y={e:X(e)=x,Y(e)=y}\begin{gather*} P(x,y)=\sum_{x,y\in V_{x,y}}P(e)\\ V_{x,y}=\{e:X(e)=x, Y(e)=y\} \end{gather*}

If i have one variable, then the other one can be inferred from the other.

P(X)=∑yP(x,y)P(Y)=∑xP(x,y)\begin{gather*} P(X)=\sum_yP(x,y)\\ P(Y)=\sum_xP(x,y) \end{gather*}