Math Problem Statement

If X v N .; 1/ derive the characteristic function of X2:

Solution

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Math Problem Analysis

Mathematical Concepts

Probability Theory
Characteristic Function
Fourier Transform
Gaussian Distribution

Formulas

Characteristic function: φ_X(t) = E[e^{itX}]
Gaussian integral: ∫ e^{-ax^2} dx = √(π/a) for a > 0

Theorems

Characteristic function of a random variable
Gaussian integral theorem

Suitable Grade Level

Undergraduate - Probability and Statistics