The moment generating function is
$M_X(t)=$$\int_{-\infty}^{\infty} e^{tx}f(x) dx$ if X is continuous.
2026-02-23 02:51:08.1771815068
How to show a continuous random variable with even pdf also has a even moment generating function?
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Hint: change of variables $u = -x$ in the integral.