Probability distribution is an essential concept in statistics, helping us understand the likelihood of different outcomes in a random experiment. Whether you’re a student, researcher, or professional ...

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 ...

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 ...

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

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, ...

Abstract: Traditionally, the uncertainty qualification is utilized with the known probability distribution function (PDF). However, in some scenarios, the PDFs of some uncertain variables are modeled ...

Let $\xi_1, \xi_2, \cdots$ be independent random variables. The distribution of $\max (0, \xi_1, \xi_1 + \xi_2, \cdots, \xi_1 + \cdots + \xi_n)$ is investigated by means of a method based on the ...