Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Stochastic Processes
Wiener Process
Probability Theory

Formulas

E[|Z|] = σ * sqrt(2/π) for Z ~ N(0, σ^2)
Var(|Z|) = σ^2(1 - 2/π) for Z ~ N(0, σ^2)
Mean of Y_n = sqrt(2^n / π)
Variance of Y_n = 1 - 2/π

Theorems

Wiener Process Properties
Normal Distribution
Independence of Increments

Suitable Grade Level

University (Advanced Undergraduate/Graduate level)