Let $X_1, X_2..$ be a sequence of independent log-normally distributed random variables. Prove that there exists a constant $c\in\mathbb{R} $ such that $$\lim_{n \to \infty}\sqrt[n]{\prod_{i=1}^{n}X_i} = c\space\space\space[\mathbb{P}]$$
2026-03-27 03:45:25.1774583125
Sequence of log-normal distributed random variables
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