Let Y1, Y2, . . . , Yn be independent, uniformly
Chapter 6, Problem 76E(choose chapter or problem)
Problem 76E
Let Y1, Y2, . . . , Yn be independent, uniformly istributed 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.
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