Question: Markov inequality Let X1 , . .. . Xn N (H, 62), let Fn (1) = = n 1=1 denote their empirical distribution, and let

Markov inequality

Let X1 , . .. . Xn N (H, 62), let Fn (1) = = n 1=1 denote their empirical distribution, and let @,2 denote the cdf of the distribution N (1, 62). Recall that in the Kolmogorov-Smirnov test, we considered the test statistic T, = Vn sup |F, (1) - @,.621 ER In the Kolmogorov-Lilliefors test, we consider the test statistic Tn = Vnsup |F, (1) - Qua IER It is true or false that T, and T' , have the same distribution for for all n E N? (Refer to the slides.) O True FalseLet {Xiji=1 36 be the sequence of continuous IIDRV with EXi = 40, Var Xi = 144, i = 1, ..., 36 and A36 Eil Xi = 36 (a) By using the Markov's inequality estimate P( A36

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