What exactly is a random variable? - Mathematics Stack Exchange
Mar 27, 2018 · 17 A random variable is nothing more or less than a function on a probability space with values in $ {\mathbf R}$. First we need to be clear about what a probability space …
What does the definition of a random variable actually mean?
Apr 8, 2022 · The random variable is just a function of the outcome $\omega$. Most functions that you can think of would probably meet the technical definition of a random variable.
Understanding definition of a continuous random variable
Jul 27, 2024 · The outcomes of experiments are represented by the points on line segments or lines, and the values of random variables are numbers appropriately assigned to the points by …
Discrete and Continuous variables. What is the definition?
Sep 13, 2021 · A random variable is a function that maps a sample space to the real numbers. A continuous random variable is such a function such that it can take on any value in an interval …
self study - Intuition about the definition of random variables ...
Jul 23, 2021 · A random variable or stochastic variable is a value that is subject to chance variation (i.e., randomness in a mathematical sense) whereas in the Wikipedia article, for …
Precise definition of the support of a random variable
Associated with each random variable is a probability density function (pdf) for the random variable. The sample space is also called the support of a random variable.
What is it meant with the $\sigma$-algebra generated by a …
Often, in the course of my (self-)study of statistics, I've met the terminology "$\sigma$-algebra generated by a random variable". I don't understand the definition on Wikipedia, but most …
What is the difference between sample space and random variable?
I was going through this article and, on this page, I encountered the definition of a random variable and a sample space. According to this page: A random variable is a set of possible …
Confusing random variable definition - Mathematics Stack Exchange
Aug 31, 2023 · A continuous random variable is associated with a real value. This definition seems to be different from the regular definition of a random variable, which from my …
measure theory - What's the difference between a random …
Apr 26, 2015 · Thus, random variables would be measurable functions defined on a probability space, or, to summarize: random variable = measurable function + probability measure.