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In: Statistics and Probability

Let U, V be iid Unif(0, 1) random variables, and set M = max(U,V) and N...

Let U, V be iid Unif(0, 1) random variables, and set
M = max(U,V) and N = min (U,V)

(a) Find the conditional density of N given M = a for any value of a ∈ (0, 1).

(b) Find Cov(M, N).

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