Random Variables vs Events

• a random variable 𝑋 is a real-valued function 𝑋 : 𝛺 → ℝ where 𝛺 is the sample space
• an event 𝐸 is a subset of 𝛺

Example

The value of 2 dice rolls. For example (1,4)∊𝛺, then:

• A random variable 𝑋 can be defined as the sum of the value of 2 dice rolls
• An event 𝐸 can be defined as {𝑋 = 4} that is the event of all possible outcomes 𝜔 in 𝛺 that are mapped to 𝑋(𝜔) = 4
  • thus 𝐸 = {(1,3), (3,1), (2, 2)}