So far, you learned about discrete random variables and how to calculate or visualize their distribution functions. In this lesson, you'll learn about continuous variables and probability density ...

What Is A Probability Density Function? A probability density function, also known as a bell curve, is a fundamental statistics concept, that describes the likelihood of a continuous random variable ...

The joint probability density function \(f\) of two random variables \(X\) and \(Y\) satisfies, for every \(a_1 b_1\) and \(a_2 b_2\), \[ P(a_1\le X\le b_1, a_2\le Y ...

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 ...

On a certain track team, the runners all take between 4 and 7 minutes to finish a mile. Suppose the probability density function for the length of time it takes a ...

The Probability Distributions Explorer is a web-based application that helps users understand various statistical distributions through visualization and interactive parameter manipulation. The ...

In many experimental observation systems where the goal is to record a three-dimensional observation of an object, or a set of objects, a lower-dimensional projection of the intended subject is ...