Moreover, since all probabilities for X and Y of the type appearing in Eq. (3.5.3) can be
Derived from probabilities of the type appearing in Eq. (3.5.4), it can be shown that if
Eq. (3.5.4) is satisfied for all values of x and y, then X and Y must be independent. The
Proof of this statement is beyond the scope of this book and is omitted. In other words,
Two random variables X and Y are independent if and only if Eq. (3.5.4) is satisfied for
All values of x and y.