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

Will Kenton is an expert on the economy and investing laws and regulations. He previously held senior editorial roles at Investopedia and Kapitall Wire and holds a MA in Economics from The New School ...

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, ...

Overview: In probability and statistics, it is important to understand the mean and variance for any random variables. In many applications, it is straightforward to simulate the random variable Y ’s, ...

A **variable** is said to be **random** if its values are determined by a random experiment. In other word, **random variable** is a numerical description of the ...

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 ...

Colorblindness is caused by a recessive gene on the X chromosome. Since men have only one X chromosome, if a man carries the colorblindness allele (gene form), he will have the trait. Women have two X ...