= 6. (Order Statistics, 4+3+3=10 points) Let 3 (1) <3 (2) <3 (3) <... 2) are order statistics from some popul

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6 Order Statistics 4 3 3 10 Points Let 3 1 3 2 3 3 N N 2 Are Order Statistics From Some Popul 1 (31.42 KiB) Viewed 113 times

= 6. (Order Statistics, 4+3+3=10 points) Let 3 (1) <3 (2) <3 (3) <... <?(n) (n > 2) are order statistics from some population. Please prove the following conclusions: (a) The Joint Probability Density Function of ((1), 1(n)) is: p(ui, u2) = n(n-1)[F(uz) - F(01))"-2p(ui)p(uz), u < u2 (Hint: Please check the proof of the pdf of order statistics in class) (b) The Cumulative Distribution Function of R = *(n) – 3(1) is: Fr)=n nſ F(r+u) – F(u)-"p(u)du, r > 0 = -00 (c) If F(x) is the Cumulative Distribution Function of Uniform Distribution U (0,1), then R = (n) - 3(1) Ben-1,2).