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 ...

In the early development of probability theory, only discrete random variables (although not called random variables at the time) were considered. Isaac Newton (1643-1727) considered the idea of ...

The range of correlation coefficient of any bivariate discrete random vector with finite or countably infinite values is derived. We show analytically that the normal-transformed discrete bivariate ...

This course enhances students' understanding of probability and statistics, essential for applications in Computer Science and data analysis. Students will learn through a combination of theory and ...

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 ...

Example 1: A coin is flipped. Random variable X takes the value 1 if the coin lands heads, and X takes the value 0 if the coin shows tails. Example 2: Three balls are drawn without replacement from a ...

Data is usually divided into two types: discrete and continuous, both of which play important roles in subjects such as statistics, mathematics, computer science, and data analysis. Understanding the ...

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