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Differentiation of a Moment Generating Function

M'(t) = (μ+tσ²) exp {½ t²σ² + μt}

m'(t) = (μ+tσ²) exp {½ t²σ² + μt} + σ²exp {½ t²σ² + μt}

m''(t) = ?? Please help


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An MGF is differentiated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.