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Order statistics of two uniforms

MediumRandom VariablesStatistics~5m

Let X,Y∼U[0,1]X, Y \sim U[0,1] be independent. What is E[max⁡(X,Y)]E[\max(X,Y)]? Give a decimal. (What about E[min⁡]E[\min]?)

Show hints (2)+
  1. Find the CDF of the max first: P(max ≤ t) = t².
  2. max + min has the same mean as X + Y.

Answer

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0.6667 (± 0.005)

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