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I've calculated the MLE of the uniform distribution on [0,theta] as maxi{Xi} but don't know how to prove it is biased. The formula I have learned to prove it is unbiased is E(θ^)-θ=0.

Was stuck on how to take expectation of max{xi} values. Any help would be appreciated, thanks.

meow
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  • Find the distribution of the maximum. Doing so requires only applying probability axioms -- no extensive calculations or theorems are needed. – whuber Nov 07 '23 at 13:47
  • @whuber can you please ellaborate on how to do so? thanks – meow Nov 07 '23 at 13:54
  • See the duplicate. Alternatively, compare the maximum to $\theta$ itself; note that the maximum almost surely is strictly less than $\theta,$ and (immediately) draw the conclusion. – whuber Nov 07 '23 at 18:20

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