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

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 ...

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 ...

Investopedia contributors come from a range of backgrounds, and over 25 years there have been thousands of expert writers and editors who have contributed. Representative sampling and random sampling ...