Two questions involving order statistics
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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)
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