Homework2_solution

Homework2_solution - Homework #2 Solutions 5.1 (a) the...

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Homework #2 Solutions 5.1 (a) the population is the uniform distribution over integers 1 to 5. The mean and variance of the population are and (b) (1,1) (1,2) (1,3) (1,4) (1,5) (2,1) (2,2) (2,3) (2,4) (2,5) (3,1) (3,2) (3,3) (3,4) (3,5) 1.0 1.5 2.0 2.5 3.0 1.5 2.0 2.5 3.0 3.5 2.0 2.5 3.0 3.5 4.0 (4,1) (4,2) (4,3) (4,4) (4,5) (5,1) (5,2) (5,3) (5,4) (5,5) 2.5 3.0 3.5 4.0 4.5 3.0 3.5 4.0 4.5 5.0 (c) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 (d) The mean of is The variance of is

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and , respectively. 5.34 Since the rth order statistic in a random sample of size n from a U[0,1] distribution has the beta distribution with parameters r and n-r+1, , , and 5.38 (a) (1,2) (1,3) (1,4) (1,5) (2,3) (2,4) (2,5) 1.5 2.0 2.5 3.0 2.5 3.0 3.5 (3,4) (3,5) (4,5) 3.5 4.0 4.5 (b) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 (c) The mean of is The variance of is (d) The finite population correction factor is . Then the variance of is . This matches the answer in (c). 6.2
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This note was uploaded on 01/31/2011 for the course AMS 572 taught by Professor Weizhu during the Fall '10 term at SUNY Stony Brook.

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Homework2_solution - Homework #2 Solutions 5.1 (a) the...

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