Probability

This lesson gives an intuitive explanation of the joint probability density function of two continuous random variables. We will mainly focus on understanding what bi-variate joint probability density functions are and then extend the concept to multivariate joint probability density functions.

This lesson uses an example of the joint probability mass function (joint PMF) of two random variables. We learn about joint probability mass functions (joint PMFs) by exploring these two discrete random variables jointly: number of goals scored by the home team in a football/soccer game, and the number of goals scored by the away/traveling team.

This lesson gives an intuitive introduction to the probability density function of a univariate continuous random variable. For a continuous random variable, the probability density function at a specific point can be thought of as the relative likelihood of observing values in a very small interval containing that specific point.