A random variable $${\displaystyle X}$$ is a measurable function $${\displaystyle X\colon \Omega \to E}$$ from a sample space $${\displaystyle \Omega }$$ as a set of possible See more

Discrete random variable
Consider an experiment where a person is chosen at random. An example of a random variable may be the person's height. … See more

The probability distribution of a random variable is often characterised by a small number of parameters, which also have a practical interpretation. For example, it is often enough to know what its "average value" is. This is captured by the mathematical … See more

• The probability distribution of the sum of two independent random variables is the convolution of each of their distributions.
• Probability … See more

If a random variable $${\displaystyle X\colon \Omega \to \mathbb {R} }$$ defined on the probability space
Recording all these … See more

The most formal, axiomatic definition of a random variable involves measure theory. Continuous random variables are defined in terms of See more

A new random variable Y can be defined by applying a real Borel measurable function $${\displaystyle g\colon \mathbb {R} \rightarrow \mathbb {R} }$$ to the outcomes of a See more