In this paper, a statistical approach is suggested to derive some properties of the classical gamma and beta functions. The main concept is to consider some density functions whose random variables are particular functions in two order statistics taken from certain parent distributions. Integrating these density functions over the whole range and equating to one, gives some properties as equalities. Making use of the positive variance of the chosen functions in the two order statistics gives other properties as inequalities. In this paper, two parent distributions are used and four choices of functions in two order statistics. Some of the derived properties may be found in literature, while the rest may not. For those properties that are found in literature, the suggested approach gives alternative proofs.