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pdf fox)=1-g2 exp( -||), TER 2 where is an unknown parameter satisfying |0| < 1 (a) (10 points) Find the joint pdf f(x,y) of (X(),X(n), x < y, where X(j) is the jth order statistic. Express f(,y) explicitly in three regions: {0 < x < y} {x<y<0},and{x<0<y}. (b) (5 points) Using Theorem 5.2.11, show that T = X +...+ X, has a pdf from an exponential family. (c) (10 points) For n = 2, show (without using Theorem 5.2.11) that the pdf of T = X + X2 is from an exponential family, using the formula for the pdf of a sum of two random variables. (Hint: you may leave an integral in the formula of the pdf and still argue that the pdf is from an exponential family.

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fox)=1-g2 exp( -||), TER 2 where  is an unknown parameter satisfying |0| < 1
(a) (10 points) Find the joint pdf f(x,y) of (X(),X(n), x < y, where X(j) is the jth order statistic. Express f(,y) explicitly in three regions: {0 < x < y} {x<y<0},and{x<0<y}. (b) (5 points) Using Theorem 5.2.11, show that T = X +...+ X, has a pdf from an exponential family.
(c) (10 points) For n = 2, show (without using Theorem 5.2.11) that the pdf of T = X + X2 is from an exponential family, using the formula for the pdf of a sum of two random variables. (Hint: you may leave an integral in the formula of the pdf and still argue that the pdf is from an exponential family.

pdf fox1 g2 exp ter 2 where is an unknown parameter satisfying 0 1 a 10 points find the joint pdf fxy of xxn x y where xj is the jth order statistic express fy explicitly in three regions 0 60982

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