A New Direct Proof of the Central Limit Theorem
Dobric, Vladimir · Garmirian, Patricia
Original · EN
We prove the Central Limit Theorem (CLT) from the definition of weak convergence using the Haar wavelet basis, calculus, and elementary probability. The use of the Haar basis pinpoints the role of L²([0,1]) in the CLT as well as the assumption of finite variance. We estimate the rate of convergence and prove strong convergence away from the tails.
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