An Example of Bias

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Suppose that a random variableis known to be uniform so thatA sample of size n is taken and the maximumis recorded so that

Given any number 0<x<a, the probability thatis

The probability thatandis

The probability thatandis

Continuing in this way, for the sample of sizethe probability that all theare less thanisso that

The probability density functionis

The expectation value ofis

The bias is then

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