Math Problem Statement

) 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 .

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Independent Identically Distributed Random Variables
Limit of a Sequence
Exponentials

Formulas

lim(n→∞) (∏(i=1)^n Yi)^(1/n)

Theorems

Strong Law of Large Numbers

Suitable Grade Level

University Level