Explain with solid detail why the moment-generating function Mx(t) = Ex (e^t) does not always exist while the characteristic function +(€) Ex (e^ix) exists for any random variable.
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- The moment-generating function (MGF) of a real random variable X is M_X(t) = E[e^{tX}] (for real t), provided this expectation is finite. - The characteristic function (CF) of X is φ_X(ξ) = E[e^{iξX}] (for real ξ). Existence means the complex expectation is Show more…
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