The total area under the curve must equal 1, representing the fact that the probability of some outcome occurring within the entire range is certain. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

Density functions are nonnegative for all real numbers but greater than zero only at a finite or countably infinite number of points. Density functions are nonnegative for all real numbers and are ...

Amusement park patrons, wanting to go on a log ride, might not have to wait in line at all, they might have to wait for hours, or the wait could be anywhere in between. For a random log rider, the ...

So far we have looked at discrete random variables and how to calculate/visualize their distribution functions. In this lesson, we shall deal with continuous variables and probability density function ...

In this repo, I prensent you a tool that can make samples from a random variable given by it's density fuunction. The density function can be whatever you want even thought i has a finite integral il ...

Abstract: In this chapter, we introduce the concept of a random variable and develop the procedures for characterizing random variables, including the cumulative distribution function, as well as the ...

The main property of a discrete joint probability distribution can be stated as the sum of all non-zero probabilities is 1. The next line shows this as a formula. The marginal distribution of X can be ...