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Let X, Y ∼ U[0, 1], be independent and let Z = max{X, Y }. (a)...

Let X, Y ∼ U[0, 1], be independent and let Z = max{X, Y }. (a) (10 points) Calculate Pr[Z ≤ a]. (b) (10 points) Calculate the density function of Z. (c) (5 points) Calculate V ar(Z).

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