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Just as the picture below, Can I get some help? (a) Let U1 = X1, Ui = Xi Xi1, i = 2, 3, ..., n. Find the joint pdf of (U1, U2, ..., Un). (b) Are U1,


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Just as the picture below, Can I get some help?

(a) Let U1 = X1, Ui = Xi − Xi−1, i = 2, 3, ..., n. Find the joint pdf of (U1, U2, ..., Un).

(b) Are U1, U2, ..., Un mutually independent? What is the marginal distribution of each of theUi, i = 1, 2, ..., n?

(c) Using the result of part (a) and (b), or otherwise, find E[X1] and E[Xn], the expectation of thesample minimum and sample maximum.

 


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