Question

Central limit theorem implies weak law of large numbers

Answer 1

$\huge\mathfrak\red{Heya\:Mate}$

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The central limit theorem as stated by the OP does not imply the weak law of large numbers. As n → ∞ , the OP's version of the central limit theorem says that. Z n − μ > σ } → 0.317 ⋯ while the weak law says that