Random Variables and Univariate Probability Distributions Random Variables Random Variables It is inconvenient to work with different sample spaces. To develop a unified probability theory,we consider a mapping X from the original sample space S to a new sample space which consists of a set of real numbers. This transformation X:S->is called a random vari- able. In many applications,we may be interested only in some particular aspect of the outcomes of an experiment,rather than the outcomes themselves.A suitably defined ran- dom variable X will better serve for our purpose. Random Variables and Univariate Probability Distributions Introduction to Statistics and Econometrics May23,2019 3/287Random Variables and Univariate Probability Distributions Random Variables and Univariate Probability Distributions Introduction to Statistics and Econometrics May 23, 2019 3/287 Random Variables Random Variables