In this lecture, we start our discussion of continuous random variables.
We will focus on the case of a single continuous random variable, and we’ll describe its distribution using a so-called probability density function, an object that will replace the PMFs from the discrete case.
We will then proceed to define the expectation and the variance of a continuous random variable, and we’ll see that their basic properties remain unchanged.
There will be one new concept– the cumulative distribution function, which will allow us to describe, in a unified manner, both discrete and continuous random variables, even so-called mixed random variables that have both a discrete and a continuous component.
In the course of this lecture, we will also introduce some of the most common continuous random variables– uniform, exponential, and normal.
We will pay special attention to the normal distribution and the ways that we can calculate the associated probabilities.
