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 ...

The first step is to ensure that the given distribution actually is a valid probability distribution. As mentioned earlier, ...

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 ...

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 ...

A discrete random variable is a type of random variable that can take on a countable set of distinct values. Common examples include the number of children in a family, the outcome of rolling a die, ...

In a raffle with 20 tickets, 6 tickets are drawn for prizes. The first prize winner gets $\$20$, 2 second prize winners get $\$10$, and three third prize winners get $\$5$. What is the sample space ...

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 ...

Forecasting for any small business involves guesswork. You know your business and its past performance, but you may not be comfortable predicting the future. Using Excel is a great way to perform what ...