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 ...

A Probability Density Function (PDF) helps identify the regions in the distribution where observations are more likely to occur, in other words, where the observation occurrence is more dense. It is ...

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 ...

Department of Basic Science, Nippon Veterinary and Life Science University, Tokyo, Japan. According to the uncertainty principle, the motion of the single electron in the 1s orbit of a hydrogen atom ...

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 ...

In the board game "Chick-a-Pig," a cow that sits in the center of the board and creates an obstacle for players attempting to move across the board. On each turen, a player rolls a die to determine ...