A random variable is a variable whose possible values are numerical outcomes of a random phenomenon. It is a fundamental concept in probability and statistics, used to quantify and analyze random ...

Roll a die and ask students to identify the random variable. Since a die can only take on values of 1, 2, 3, 4, 5, or 6, this is a discrete random variable. Repeat ...

A continuous random variable is a type of variable that can take on any value within a given range. Unlike discrete random variables, which have a countable number of outcomes, continuous random ...

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 ...

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 ...

This paper considers a class of simultaneous equation models with both discrete and continuous random variables based on normally distributed latent random variables. The model set forth here contains ...

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 ...

ABSTRACT: This in virtue of the notion of likelihood ratio and the tool of moment generating function, the limit properties of the sequences of random discrete random variables are studied, and a ...