Let X1, X2 ,X3 ∼U[0,1] be independent, and letX(1),X(2),X(3) be the order statistics, i.e., X(1) <...

Let X₁, X₂ ,X₃ ∼U[0,1] be independent, and letX₍₁₎,X₍₂₎,X(3) be the order statistics, i.e., X(1) < X(2) < X(3)

(a) Find f₍₁₎(x), f₍₂₎(y) and f₍₃₎(z).

(b) Verify that the joint density of X₍₁₎ and X₍₂₎ is

f_(1,2)(x,y)=6(1−y), 0

(c) Find the conditional density of X(1) given X(2).

(d) Find E(X₍₁₎+X_{(3 )}/ X₍₂₎)

Expert Solution

orchestra answered 2 years ago

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