LOTUS on a uniform

What this LOTUS probability question tests

This is a straightforward but instructive probability question that asks you to compute an expectation using the Law of the Unconscious Statistician (LOTUS) — one of the most practical tools in probability. It probes whether you can apply LOTUS directly without unnecessarily deriving a transformed distribution.

The question rewards efficient reasoning: rather than finding the PDF of U² and then integrating, you work directly with the original uniform distribution and the function of interest. This is exactly how practitioners approach expectation problems in quant finance and data science.

• Law of the Unconscious Statistician (LOTUS) for continuous random variables
• Integration of polynomial functions over finite intervals
• When to avoid unnecessary distribution transformations