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Two questions involving order statistics

1. Ten observations of X are

67 6 7 35 78 28 74 5 9 37

a) Find the order statistics
b) Find the median and 80th percentile of the sample
c) Determine the first and third quartiles of the sample

2. Let Y1<Y2<Y3<Y4<Y5 be the order statistics of 5 independent observations of an exponential distribution with mean 3.

a) Find the pdf of the sample median Y3
b) Compute the probability that Y4 is less than 5
c) Determine P(1<Y1)

(See attachment for questions in full with mathematical notation)

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Solution Summary

The solutions are given in a Word attachment with equations written in Mathtype. Each solution is explained step-by-step and calculations are worked rather than being calculated by computer or calculator.