CS 70 Discrete Mathematics and Probability Theory

Spring 2015 Vazirani Note 20

A Brief Introduction to Continuous Probability

Up to now we have focused exclusively on discrete probability spaces , where the number of sample points

is either nite or countably innite (such as the integers). As a consequence, we have only been able

to talk about discrete random variables, which take on only a nite or countably innite number of values.

But in real life many quantities that we wish to model probabilistically are real-valued; examples include

the position of a particle in a box, the time at which an certain incident happens, or the direction of travel

of a meteorite. In...