Maurice Tutor

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Teaching Since: May 2017
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  • MCS,PHD
    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

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  • Professor
    Phoniex University
    Oct-2001 - Nov-2016

Category > Management Posted 11 Feb 2018 My Price 7.00

joint density function

Let Y1, Y2, . . . , Yn be independent, uniformly distributed random variables on the interval [0,θ].

a Find the joint density function of Y( j ) and Y(k) where j and k are integers 1 ≤ j k ≤ n.

b Use the result from part (a) to find Cov(Y( j ), Y(k)) when j and k are integers 1 ≤ j k ≤ n.

c Use the result from part (b) and Exercise 6.76 to find V(Y(k) − Y( j )), the variance of the difference between two order statistics.

Exercise 6.76

Let Y1, Y2, . . . , Yn be independent, uniformly distributed random variables on the interval [0,θ].

a Find the density function of Y(k), the kth-order statistic, where k is an integer between 1 and n.

b Use the result from part (a) to find E(Y(k)).

c Find V(Y(k)).

d Use the result from part (c) to find E(Y(k) − Y(k−1)), the mean difference between two successive order statistics. Interpret this result.

Answers

Maurice Tutor
(5)
Status NEW Posted 11 Feb 2018 12:02 AM My Price 7.00

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