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Unformatted text preview: . 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 1 , X 2 , … , X n be i.i.d. Exponential ( λ ). That is, suppose the p.d.f. of X i is f X i ( x ) = λ e – λ x , x > 0, i = 1, 2, … , n . a) Find the probability distribution of max X i . b) Find the probability distribution of min X i . 4. Let X i be an Exponential ( λ 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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This note was uploaded on 02/11/2011 for the course STAT 410 taught by Professor Monrad during the Spring '08 term at University of Illinois, Urbana Champaign.
- Spring '08