A probability distribution of a random variable describes how the probabilities are distributed over the possible values of the random variable. A probability distribution shows the likelihood of ...

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. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

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 probability distribution of a random variable, often denoted as x, is simply called a distribution, a cornerstone concept in probability theory and statistics. It provides a complete description ...

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 ...

In this lesson, you'll look at a way to represent discrete distributions - the probability mass function (PMF), which maps from each value to its probability. A probability mass function (PMF), ...