Question: 9.6.2 Let X I , . . . , X , be independent variables with a U[O, 11 distribution. The joint density of the X

9.6.2 Let X I , . . . , X , be independent variables with a U[O, 11 distribution. The joint density of the X = min(X1, . . . , X,) and Y = max(X1, . . . , X,) has density f(x, y) = n(n - l ) ( y - x)n-2 for 0 5 x 5 y 5 1 and f(x, y) = 0 otherwise. Find:

(i) E ( X m ) ,E ( Ym)

a, n d p ( X ,Y ) .( ii) E( Y 1X) .

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