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If $X$ follows normal distribution with mean $\mu$ and variance $\sigma^2$, then the moment generating function of $X$ is given by: $$M_X(t) = e^{\mu t + \frac{1}{2}\sigma^2t^2}.$$

Then how can I find the pdf of $\dfrac{1}{X}$ using moment generating function technique?

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Why do you want to use MGF to find the PDF of 1/X? –  Did Apr 28 '13 at 11:39
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