Continuous Probability

This chapter aims to define the terms: continuous RV, probability density function, and cumulative density function. It provides problems involving joint and marginal distributions in the continuous setting. One way to connect and unify the treatment of discrete and continuous random variables is through the cumulative distribution function which is defined for all random variables. Formulas for expectation and variance for continuous random variables follow as expected from the discrete formulas: integrals replace sums and probability density function replace probability mass functions (pmf). An important property of the exponential distribution is memorylessness. The chapter introduces many concepts for discrete probability, such as expectation, variance, joint and conditional distributions, extend naturally to the continuous framework. For two or more random variables, the joint density function or joint pdf plays the role of the joint pmf for discrete variables.