Uniform on the unit square

Computing probabilities and marginal densities for uniform distributions

This is an easy warm-up question in probability and statistics that tests your ability to work with uniform distributions over a 2D region. It asks you to find both a geometric probability (the chance that two uniform random variables satisfy a linear constraint) and to derive a marginal density by integration.

Questions like this are common early in interviews because they confirm you can visualize a probability problem geometrically, set up and evaluate a double integral, and reason about marginal distributions from a joint density. The problem rewards clear setup and careful integration over correct bounds.

• Joint uniform distributions and constant density over a region
• Geometric probability and area arguments
• Deriving marginals by integrating out variables