Random Variable

A Mapping from the Sample Space to the Real Numbers. Used to assign numbers to outcomes. Random variables are denoted by capital letters like $X,Y,Z$ and their outcomes denoted as lowercase $x,y,z$.

Set of Random Variables Notation

Random variables are used ‘in reverse’ to describe events (Set of outcomes for which maps to our number of interest $b$)

Defining events using a random variable: $A=\{s\in S:X(s)=b\}=\{X=b\}$

Properties

A random variable is:

1. A countable quantity
2. A depiction of an independent trial out of a larger # of trials.
3. Has fixed # of trials For a random variable X, the variable x are the separate outcomes that X can be.

Types of Random Variables

• Discrete Random Variable
• Continuous Random Variable