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

Amusement park patrons, wanting to go on a log ride, might not have to wait in line at all, they might have to wait for hours, or the wait could be anywhere in between. For a random log rider, the ...

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 ...

Abstract: We establish the first known upper bound on the exact and Wyner's common information of n continuous random variables in terms of the dual total correlation between them (which is a ...

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 ...

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 ...

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 ...