Question: 21. Let X and Y be independent random variables, each uniformly distributed on [0, 1]. Let U = min{U, V} and V = max{U, V}.

21. Let X and Y be independent random variables, each uniformly distributed on [0, 1]. Let U =

min{U, V} and V = max{U, V}. Show that E(U) = 1 3 , and hence find the covariance of U and V . (Cambridge 2007)

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