Question: 4. Let X, X, X, be a random sample from U(0,1). Let Y,,, Y, be the order statistics based on X, X, , X5.

4. Let X, X, X, be a random sample from U(0,1). Let Y,,, Y, be the order statistics based on X, X, , X5. (a) Determine the distribution of the sample median X. (b) Find P(Y,> 0.5). (c) Determine the distribution of R=Y, - Y. (d) Find E(R) and Var(R).

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