Roll a die and ask students to identify the random variable. Since a die can only take on values of 1, 2, 3, 4, 5, or 6, this is a discrete random variable. Repeat ...

A continuous random variable is a type of variable that can take on any value within a given range. Unlike discrete random variables, which have a countable number of outcomes, continuous random ...

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 ...

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, ...

The Virginia Lottery offers a game called the New Year's Millionaire Raffle for which the top prize is one million dollars. There are 375,000 tickets sold, of which 508 are winners. There are three ...

The reports aim to provide a clear understanding of key concepts in probability and statistics, making them accessible to learners at all levels. Each report breaks down complex topics into digestible ...

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 ...

Abstract: Mixed type random variables contain both continuous and discrete components, and their role is critical in many well-studied fields. Queuing analysis, stock options, and hydrology rainfall ...