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 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 ...

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 ...

Abstract: Consider a system comprising sensors that communicate with a remote estimator by way of a so-called collision channel. Each sensor observes a discrete random variable and must decide whether ...

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 ...

College of Mathematics and Physics, Shijiazhuang University of Economics, Shijiazhuang, China. Science College, Beijing University of Civil Engineering and Architecture, Beijing, China. [1] W. Liu, ...

Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding ...