Lecture Probability Theory - Lecture 5: Function of a Random Variable. Let Y be a random variable, discrete and continuous, and let g be a function from R to R, which we think of as a transformation. For example, Y could be a height of a randomly chosen person in a given population in inches, and g could be a function which transforms inches to centimeters, . g(y) = × y. Then W = g(Y) is also a random variable, but its distribution (pdf), mean, variance, etc. will differ from that of Y. Transformations of random variables play a central role in statistics, and we will learn how to work with them in this section. |
