🎲 Random Variables

Expectation problem

Assign a real value to each outcome in a probability experiment.

Theory:

A random variable $X$ assigns a number to each outcome in the sample space $S$:

$$X:S\to \mathbb{R}$$

The expected value (mean) of a random variable is:

$$E[X]=\sum _{x\in S}x\cdot P(x)$$

Where $P(x)$ is the probability of outcome $x$.