Let X 1 , brvbar , X n be independent identically distributed (i i d ) r v s defined on the probability space (W, A , P ) and having d f F Let F n be empirical d f defined in terms of the Xi s i e , Then show that is a r v That is, although D n ( Atilde ) is arrived at through non countable operations, it is still a r v Define Fn(x, w) number of X1( ), , X( ) x ,

Question: Let X 1 ,¦, X n be independent identically distributed (i.i.d.) r.v.s defined on the probability space (W, A , P ) and having d.f.

LetX₁,€¦,X_nbe independent identically distributed (i.i.d.) r.v.s defined on the probability space (W,A,P) and having d.f.F. LetF_nbe empirical d.f. defined in terms of theXis; i.e.,

Fn(x, w) = -[number of X1(@), ..., X„(@) < x], п

Then show that

Let X1,..., Xn be independent identically distributed (i.i.d.) r.v.s defined

is a r.v. That is, although D_n(Ã—) is arrived at through non-countable operations, it is still a r.v.

Define

Let X1,..., Xn be independent identically distributed (i.i.d.) r.v.s defined

Fn(x, w) = -[number of X1(@), ..., X(@) < x],

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