Abstract
I consider the calculation of the probability $P_n$ that the graph of a sample distribution function lie wholly to one side of a given arbitrary contour. A generating function approach is described in Section 2, and $P_n$ calculated exactly for some simple types of contour. Upper and lower bounds of the correct asymptotic form (relations (14), (15)) are obtained for $P_n$ in the case of a straight line contour.
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