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Suppose $X$ has the standard normal distribution and $Y$ has an exponential distribution. How would you find the mgf of $\frac{X}{\sqrt{Y}}$? Would it be $$ \frac{M_{X}(t)}{\sqrt{M_{Y}(t)}}$$

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    The moment generating function would be $\mathbb{E}[e^{tX/\sqrt{Y}}]$, which is not the same as $\mathbb{E}[e^{tX}]/\sqrt{\mathbb{E}[e^{tY}]}$.2012-05-17

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