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Finding the expected value of the maximum of uniform random variables

This is an easy probability question that tests your ability to work with order statistics and expected values. It is a common warm-up at quant trading and finance interviews, since it combines basic understanding of uniform distributions with the concept of the maximum of a sample.

To solve problems like this, you need to find the cumulative distribution function (CDF) of the maximum, then derive its probability density function (PDF) and compute the expectation. The key insight is that the maximum of independent random variables has a CDF equal to the product of the individual CDFs—a fact that simplifies the calculation considerably. Once you have the PDF, integration yields a clean closed-form answer.

• CDF and PDF of order statistics
• Expectation via integration
• Properties of the uniform distribution