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7. Let U1, . . . , Un be a random sample from the Uniform(0, θ)...

7. Let U1, . . . , Un be a random sample from the Uniform(0, θ) distribution.

(a) Find the joint density of order statistics U(1) and U(n) .

(b) Find the joint density of the random variables R = U(1)/U(n) and M = U(n) .

(c) State whether R and M are independent.

(d) Give the marginal pdf of R and identify the distribution

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