) Let {Yn, n ∈ N} be a sequence of independent, identically distributed random variables. Assume that Y1 = e X where X is a standard normal random variable. Use the Strong Law of Large Numbers to find the following limit limn→∞ (∏n i=1 Yi )1/n = limn→∞ (Y1 · Y2 · · · Yn) 1/n .

To solve this problem, we are asked to find the limit:

\[
\lim_{n \to \infty} \left( \prod_{i=1}^n Y_i \right)^{1/n} = \lim_{n \to \infty} (Y_1 \cdot Y_2

Let {Yn, n ∈ N} be a sequence of independent, identically distributed random variables. Assume that Y1 = e^X where X is a standard normal random variable. Use the Strong Law of Large Numbers to find the following limit lim(n→∞) (∏(i=1)^n Yi)^(1/n) = lim(n→∞) (Y1 · Y2 · · · Yn)^(1/n).

Explore how to find the limit of the sequence (Yn) of independent, identically distributed random variables given Y1 = e^X, where X is a standard normal random variable. This solution applies the Strong Law of Large Numbers to compute lim(n→∞) (∏(i=1)^n Yi)^(1/n). Suitable for advanced probability and statistics studies.

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