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Unformatted text preview: distribution with the p.d.f. f ( x ) = 3 / x 4 , x > 1. Let Y k = k th smallest of X 1 , X 2 , , X n . a) Find P ( Y 4 < 1.75 ) = P ( max X i < 1.75 ). b) Find P ( Y 4 > 2 ) = P ( max X i > 2 ). c) Find P ( Y 1 > 1.25 ) = P ( min X i > 1.25 ). d) Find P ( 1.1 < Y 1 < 1.2 ) = P ( 1.1 < min X i < 1.2 ). e) Find P ( 1.1 < Y 2 < 1.2 ). 2. Let X 1 , X 2 , , X n be a random sample ( i.i.d. ) from Uniform ( , a ) probability distribution. Let Y k = k th smallest of X 1 , X 2 , , X n . Find E ( Y k ). 3. Let X i be an Exponential ( i ) random variable, i = 1, 2, , n . Suppose X 1 , X 2 , , X n are independent. Find the probability distribution of min X i ....
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- Summer '08