Sampling from probability distributions with known density functions (up to normalization) is a fundamental challenge across various scientific domains. From Bayesian uncertainty quantification to ...

Discrete and continuous distributions are fundamental concepts in probability and statistics. Discrete distributions describe outcomes that take on distinct, separate values, such as the number of ...

Abstract: In this chapter, we introduce the concept of a random variable and develop the procedures for characterizing random variables, including the cumulative distribution function, as well as the ...

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 ...

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 ...