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 .
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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 .
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