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problemset39

# problemset39 - E X(1 b Find the expected value of the...

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STAT/MA 416 December 7, 2011 Problem Set 39 Name: 1. Consider X 1 ,X 2 ,X 3 ,X 4 which are independent and uniformly distributed on [0 , 20]. a. Find the density of the ﬁrst order statistic, i.e., ﬁnd f X (1) ( x 1 ). b. Find the density of the second order statistic, i.e., ﬁnd f X (2) ( x 2 ). 1

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2. Same setup as Question #1. a. Find the expected value of the ﬁrst order statistic, i.e., ﬁnd E ( X (1) ). b. Find the expected value of the second order statistic, i.e., ﬁnd E ( X (2) ). 2
3. Let X 1 and X 2 be the waiting times for Alice and Bob until their respective phones ring. Assume that X 1 ,X 2 are independent exponentials, each with mean 10. a. Find the density of the ﬁrst order statistic, X (1) , i.e., ﬁnd f X (1) ( x 1 ). b. Find the density of the second order statistic, X (2) , i.e., ﬁnd f X (2) ( x 2 ). 3

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4. Same setup as Question #3. a. Find the expected value of the ﬁrst order statistic, i.e., ﬁnd

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Unformatted text preview: E ( X (1) ). b. Find the expected value of the second order statistic, i.e., ﬁnd E ( X (2) ). 4 5. Let X 1 ,X 2 be independent, identically distributed, each with density f X ( x ) = 6( x-x 2 ) for 0 < x < 1, and f X ( x ) = 0 otherwise. a. Find the density of the ﬁrst order statistic, X (1) . b. Find the expected value of the ﬁrst order statistic, i.e., ﬁnd E ( X (1) ). 5 6. Design your own problem and solution. Create your own problem about order statistics. Design your problem in such a way that you would ﬁnd it enjoyable and also interesting (i.e., not completely trivial) if you found this problem in a probability book. Please provide the answer for your problem too. 6...
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problemset39 - E X(1 b Find the expected value of the...

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