Suppose that X1,...,Xn form a random sample with unknown
Chapter 10, Problem 13(choose chapter or problem)
Suppose that X1,...,Xn form a random sample with unknown c.d.f. F. Prove the claim made after Eq. (10.6.4) that the distribution of the statistic D n, given that the null hypothesis in (10.6.3) is true, is the same for all continuous F. Hint: Let Zi = F(Xi) for i = 1,...,n, and consider testing the null hypothesis that Z1,...,Zn have the uniform distribution on the interval [0, 1]. Show that the statistic D n for this modified problem is identical to the original D n
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