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 ...

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 ...

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 ...

A random variable that can take only a certain specified set of individual possible values-for example, the positive integers 1, 2, 3, . . . For example, stock prices are discrete random variables, ...

The random variable 2−3X is of the form aX+b, with a=−3 and b=2. Thus, Var(2−3X)=(−3)2Var(X)=9⋅2=18. Is it always true that $E[X^2]≥(E[X])^2$? We know ...

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 ...

Abstract: The paper deals with linear information inequalities valid for entropy functions induced by discrete random variables. Specifically, the so-called conditional Ingleton inequalities are in ...