# Random Variable

A random variable is a variable whose values depend on outcomes of a random process. It is a mathematical function that assigns a numerical value to each outcome in a sample space of a random experiment.

**Definition**

A random variable $\mathcal{X}$ is a function from the sample space $\Omega$ to the set of real numbers $\mathbb{R}$:

$\mathcal{X}: \Omega \rightarrow \mathbb{R}$**Types of Random Variables:**

**Discrete Random Variable:**Takes specific, discrete values.**Example:**The number of heads when flipping a coin 10 times. You can get 0, 1, 2, ..., or 10 heads, but not 3.5 heads.

**Continuous Random Variable:**Takes on an infinite number of possible values.**Example:**The time it takes to run a race. It could be 12.3 seconds, 12.31 seconds, 12.315 seconds, etc.