Random Variables Review

Statistics · Axiom Academy

LESSON Random Variables Review Understanding discrete and continuous random variables, probability distributions, PMF, and PDF Random variables are fundamental building blocks in probability and statistics. They provide a mathematical framework for describing uncertain outcomes by mapping sample spaces to numerical values. In this lesson, we'll review the key concepts and properties that distinguish discrete from continuous random variables. Random variables map outcomes to numbers Two types: discrete (countable values) and continuous (interval values) Capital letters denote the variable, lowercase the realized value 2 Discrete Random Variables & PMF 3 Continuous Random Variables & PDF Standard deviation: σ = √Var(X) Discrete vs. Continuous Comparison: Discrete: Countable values, PMF gives exact probabilities, summation for calculations Continuous: Interval values, PDF requires integration, P(X = x) = 0 Both: Have expected value, variance, and cumulative distribution functions (CDF)

This is the written version of the interactive lesson above. See the full Statistics course.