Functions of Random Variables

              Often we have to consider random variables which are functions of other random variables. Let be a random variable and is a function. Then is a random variable. We are interested to find the pdf of . For example, suppose represents the random voltage input to a full-wave rectifier. Then the rectifier output is given by . We have to find the probability description of the random variable . We consider the following cases:  

(a)   is a discrete random variable with probability mass function .
                The probability mass function of is given by