CDF of two coin flips

Understanding the CDF of a discrete random variable

This is an easy introductory question on probability distributions. It tests whether you can construct both a probability mass function (PMF) and cumulative distribution function (CDF) for a simple discrete random variable, then evaluate the CDF at a specific point.

The question walks through a foundational workflow: enumerate all outcomes, assign probabilities to each, compute the PMF, and then build the CDF by accumulating those probabilities. Understanding how the CDF relates to the PMF—and what it means to evaluate it at a particular value—is essential for statistics, risk management, and quantitative analysis more broadly.

• Discrete probability distributions and symmetry
• PMF as point probabilities vs. CDF as cumulative probabilities
• Evaluating and interpreting the CDF at specific points