Unit 2 overview

Random Variables

A random variable $X$ is a function from the sample space $S$ to the real line $\mathbb{R}$. That is, $X$ is a numerical outcome of an experiment. There are two types of RVs:

• $X$ is discrete if the list of possible outcomes of $X$ is finite or countably infinite.
  
• $X$ is continuous if the list of possible outcomes of $X$ is uncountably infinite (eg: an interval).

RANDOM VARIABLES IN CONTEXT

Throughout Units 2 and 3, we’ll consider three types of random variable models that can be used to answer three types of questions. First, let $X$ be the wrist circumference and $Y$ be the height of an adult.

• Univariate models: $Y$
  How does height vary among adults?

• Joint models: $Y$ and $X$
  What’s the joint behavior, or typical combination, of wrist and height among adults?

• Conditional models: $Y$ vs $X$
  How does height depend upon wrist?