Discrete Random Variables

Probability · Axiom Academy

LESSON Discrete Random Variables Understanding functions from sample spaces to real numbers A random variable is a function that maps outcomes from a sample space to real numbers. For each outcome ω in the sample space, X(ω) gives us a real number. This allows us to work with numbers instead of abstract outcomes. Random variables come in two main types based on the values they can take: Discrete Random Variable: Takes on countable values (finite or countably infinite). Examples: number of heads in coin flips, count of customers arriving. Continuous Random Variable: Can take any value in an interval. Examples: height, temperature, time. We typically use capital letters X, Y, Z for random variables and lowercase x, y, z for their specific values. Example 1: Rolling a die: X = result of die roll, X can be 1, 2, 3, 4, 5, or 6. Example 2: Flipping 3 coins: Y = number of heads, Y can be 0, 1, 2, or 3. Example 3: Drawing cards: Z = number of aces in 5 cards, Z can be 0, 1, 2, 3, or 4.

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