Random Variables and Random Vectors

• Samples from a random variable are real numbers – A random variable is associated with a probability distribution over these real values – Two types of random variables • Discrete – Only finitely many possible values for the random variable: X ∈ {a1, a2, ..., an} – (Could also have a countable infinity of possible values) » e.g., the random variable could take any positive integer value – Each possible value has a finite probability of occurring. • Continuous – Infinitely many possible values for the random variable – E.g., X ∈ {Real numbers}