Randomly Weighted Averages: Some Aspects and Extensions

Van Assche introduced recently the concept of a random variable .uniformly distributed between two independent random variables..This is equivalent to a weighted average of the two variables, with random weights uniformly distributed. In this article we study some generalizations of Van Assche's concept and results, limited to cases in which the initial random variables have a common distribution.Simple methods of analysis, based on first principles, are employed.