# Random Variables

Lesson 5 Chapter 2

In probability theory, *the outcomes of a **random phenomenon*** determine the random variable values**. In other words,

**. We should be able to measure a random variable that provides the capability to assign probabilities to its possible values. The domain of a random variable is the sample space. For example, in the case of having a dice, only six possible outcomes are considered, as {1,2,3,4,5,6}.**

*a random variable is a variable that its values are determined with a random event*By using more precise mathematics notation, a random variable is a measurable function defined as , which is from all possible space to some event . Let's have an illustrative example. Assume we would like to roll a dice, and the measurable event space is all numbers less than 4. Here, we have , the random variable as the outcome of rolling the dice, and we define the event as .