An Example of Bias

Suppose that a random variableisknown to be uniform so thatAsample of size n is taken and the maximumisrecorded so that

Given any number 0 is

The probability thatandis

The probability thatandis

Continuing in this way, for the sample of sizetheprobability that all theareless thanissothat

The probability density functionis

The expectation value ofis

The bias is then