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, ...

In this paper, we provide Poincaré-type upper and lower variance bounds for a function g(X) of a discrete integer-valued random variable (r.v.) X, in terms of the (forward) differences of g up to some ...

The expectation or the mean of a discrete random variable is a weighted average of all possible values of the random variable. The weights are the probabilities associated with the corresponding ...

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 ...

On a certain track team, the runners all take between 4 and 7 minutes to finish a mile. The probability density function for the length of time it takes a runner to ...