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 ...

This chapter introduces the concept of random variables and discrete random vari¬ables in particular. We then discuss several important discrete probability distribu¬tions directly applicable to ...

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 ...

This manuscript presents a technique for solving a multiple-objective probabilistic fractional programming problem with discrete random variables. A multiple-objective probabilistic mathematical model ...

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 reports aim to provide a clear understanding of key concepts in probability and statistics, making them accessible to learners at all levels. Each report breaks down complex topics into digestible ...

The COS method was introduced in Fang & Oosterlee (2008) and then was applied to pricing a variety of stock options for continuous random variables. This paper adapts the Fourier-cosine series (COS) ...