Question: Let X1, X2, X3 and X4 be a random sample from population with pdf fX(x) = { x, 0 < x < 1 0, otherwise.

Let X1, X2, X3 and X4 be a random sample from population with pdf fX(x) = { x, 0 < x < 1 0, otherwise. Let X(1), X(2), X(3) and X(4) be their order statistics. (a). Find the joint pdf of X(3) and X(4). (b). Find the conditional pdf of X(3) given X(4) = x4. (c). Evaluate E[X(3)|x4].

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