Convergence concepts in probability MOC

Empirical cumulative distribution function

Given a random sample of independent and identically distributed real random variables with CDF , let count how many of are less than or equal to ; i.e.

implying . The empirical cumulative distribution function of is #m/def/prob

and converges almost surely to as , hence it is an estimator of the true CDF.

Proof

#missing/proof By Kolmogorov's law.

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