4. Let X, X, X, be a random sample from U(0,1). Let Y,,, Y, be the...

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4. Let X₁, X₂, X, be a random sample from U(0,1). Let Y₁,₂,, Y, be the order statistics based on X₁, X₂, , X5. (a) Determine the distribution of the sample median X₂. (b) Find P(Y,> 0.5). (c) Determine the distribution of R=Y, - Y₁. (d) Find E(R) and Var(R). 4. Let X₁, X₂, X, be a random sample from U(0,1). Let Y₁,₂,, Y, be the order statistics based on X₁, X₂, , X5. (a) Determine the distribution of the sample median X₂. (b) Find P(Y,> 0.5). (c) Determine the distribution of R=Y, - Y₁. (d) Find E(R) and Var(R).

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Lets break down each part of the problem step by step a Determine the distribution of the sample median Y To determine the distribution of the sample ... View the full answer