Find (a) the expectation and (b) the variance of the kth-order statistic of a sample of n independent random variables uniform on [0, 1]. The density function is given in Example C in Section 3.7.
Reference
For the case where the Xi are uniform on [0, 1], the density of the kth-order statistic reduces to
This is the beta density. An interesting by-product of this result is that since the density integrates to 1,
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