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Moment Generating Functions

Senior Quant · Probability & Statistics

Question

Define the moment generating function MX(t)=E[etX]M_X(t) = E[e^{tX}]. Derive the MGF of a N(μ,σ2)N(\mu, \sigma^2) random variable. When does an MGF fail to exist, and what does that imply about tail behaviour?
←Central Limit Theorem via Characteristic Functions
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