10 Let X1, X2, , Xn be n independently randomly selected points from the interval (0, ), 0 Prove that E(R) n 1 n 1 , where R X(n) X(1) is the range of these points Hint Use part (a) of Exercise 9 Also compare this with Exercise 18, Section 9 1 ...

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10. Let X1, X2, . . . , Xn be n independently randomly selected points from the...

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10. Let X1, X2, . . . , Xn be n independently randomly selected points from the interval (0, θ), θ > 0. Prove that E(R) = n − 1 n + 1 θ, where R = X(n) − X(1) is the range of these points. Hint: Use part

(a) of Exercise 9. Also compare this with Exercise 18, Section 9.1.

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Fundamentals Of Probability With Stochastic Processes

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Authors: Saeed Ghahramani

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10. Let X1, X2, . . . , Xn be n independently randomly selected points from the interval (0, ), > 0. Prove that E(R) = n 1 n + 1 , where R = X(n) X(1) is the range of these points. Hint: Use part...
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10. Let X1, X2, . . . , Xn be n independently randomly selected points from the...

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