Beta distribution and inferences about the beta functions

In this study, general information about the Beta function and Beta distributions were given. Usage areas of Beta distributions are specified. Moments were expressed in general. The distribution of the joint probability density function of two independent random Gamma variables and the distribution of a random sample range were found to be Beta distribution. The relations were investigated between the incomplete Beta distribution and other distributions. Incomplete Beta function could be expressed as the term of hypergeometric functions. As a result, some inferences about Beta distribution were found.