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 $$ \frac{M_{X}(t)}{\sqrt{M_{Y}(t)}}$$
MGF of random variable
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probability
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0The 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