A chi-squared random variable with ν > 0 degrees of freedom (χv2) has mgf M(t) = (1 − 2t) −ν/2 . Given that Z2 ∼ χ21, derive the mean and variance of Z2 using M(t). Confirm these results using the mgf of Z, namely MZ(t) = e1/2t2 .

A chi-squared random variable with ν > 0 degrees of freedom (χv2) has mgf M(t) = (1 − 2t) −ν/2 . Given that Z2 ∼ χ21, derive the mean and variance of Z2 using M(t). Confirm these results using the mgf of Z, namely MZ(t) = e1/2t2 .

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A chi-squared random variable with ν > 0 degrees of freedom (χ_v²) has mgf M(t) = (1 − 2t) −^ν/2 . Given that Z2 ∼ χ²₁, derive the mean and variance of Z² using M(t). Confirm these results using the mgf of Z, namely MZ(t) = e^1/2t².

A chi-squared random variable with v> 0 degrees of freedom (x²) has mgf M(t) =
(1 - 2t)-¹/2. Given that Z² ~ x², derive the mean and variance of Z² using M(t).
Confirm these results using the mgf of Z, namely Mz(t)
=
ezt²
=

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