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, ...

Convergence theorems form the backbone of probability theory and statistical inference, ensuring that sequences of random variables behave in a predictable manner as their index grows. These theorems, ...

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 ...

Stop-loss and limited loss random variables are two important transforms of a loss random variable and appear in many modeling problems in insurance, finance, and other fields. Risk levels of a loss ...

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 ...