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As the image showed, it is a problem of proving the Glivenko-cantelli theorem, but not so complicated. For the distribution F is concentrated on three mass points which means the samples are bounded. And here the empirical distribution converge in probability.Please show the process of proof in details. Thx!!!

Yanwen FANG
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  • Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. – José Carlos Santos Oct 24 '17 at 15:20
  • Let X1,X2,....Xn be i.i.d. from a distribution function F which is concentrated on three mass points a, b and c with respective probability masses pa, pb and pc (where pa + pb + pc = 1). Then show sup|Fn(x)-F(x)|=op(1) where the Fn(x) is the empirical distribution – Yanwen FANG Oct 24 '17 at 15:22

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