juniorProbability
What is a cumulative distribution function (CDF)?
Updated May 17, 2026
Short answer
CDF gives the probability that a random variable is less than or equal to a given value.
Deep explanation
The CDF F(x) = P(X ≤ x) provides a complete description of probability distribution. It is always non-decreasing and ranges from 0 to 1. For continuous variables, it is the integral of the PDF.
Real-world example
Calculating probability of delivery time being under 2 days.
Common mistakes
- Thinking CDF gives probability at a single point for continuous variables.
Follow-up questions
- What is relation between PDF and CDF?
- Is CDF always increasing?