Two - Dimensional Random Variables Conditional Probability Distribution where f (x, y) fy (y) is called the conditional density function of X, given Y, and In the discrete case, is denoted by f(x/y). P(X = x;/Y = >;)= P X = x; and Y = yj) _ Pu P( Y = Vi ) P.j Similarly,- , f ( x, y) ' fx (x ) is called the conditional density function of Y, given X, is called the conditional probability function of X, given that Y = yj . and is denoted by f(y /x). The collection of pairs, ( xup., ) where i = 1,2,3, ., is called the conditional Independent Random Variables probability distribution of X, given Y = yj . If (X, Y) is a two - dimensional discrete RV such that Similarly, the collection of pairs, \\j'pie V. Pul P(X = x;/Y = y;) = P(X = x;), for all i,j where j = 1,2,3, ..., is called the or p(x = x; and Y = Vil _ p(X = x;), for all i,j conditional probability distribution of Y, given X = X; . P ( Y = y; ) In the continuous case, or P(X = x; and Y = y}} = P(X = x,) x P(Y =y;), for all i, j P ( X = x / Y = y ) = P ( x - 5 dx