This video introduces and defines scalar real random variables, covering the sample/state space, probability of outcomes, and mapping to the real axis. Some simple examples are presented. The video then motivates the probability set function by considering the axiomatic interval of the random variable taking on a value less than or equal to a specific value. It also demonstrates using the Kolmogorov's axioms and set theory, it is possible to determine the probability of being within an interval. In the limit, it is demonstrated that the gradient of the cumulative distribution function is  important, which leads to the probability density function.  This video sets the foundations for the rest of this Chapter and indeed course.