Question: Suppose N i.i.d. random variables are generated from the same known strictly increasing absolutely continuous cdf F(). We are told only X, the maximum of

Suppose N i.i.d. random variables are generated from the same known strictly increasing absolutely continuous cdf F(·). We are told only X, the maximum of these random variables. Is there a UMP size α test of H0 : N ≤ 5 versus H1 : N > 5?

If so, find it.

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