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If $f(x) = 0.5 e^{-|x|}$ for $-\infty < x < \infty$, how would you find the moment generating function for this? Also how would you find the distribution of $Y = |X|$?

Attempt:

$$E(e^{tX}) = \int_{-\infty}^\infty f(x) e^{tx} \; dx.$$

  • 1
    Hint: continue your attempt, separating the integral into an integral on $x\lt0$, where $f(x)=\frac12\mathrm e^x$, and an integral on $x\gt0$, where $f(x)=\frac12\mathrm e^{-x}$.2012-02-28
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    I get (1/(t-1))*(e^infinity -1) when x is positive. I am not sure what I am doing wrong.2012-02-28
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    The pdf doesn't integrate to one. I think there is a .5 in the exponential term.2012-02-28

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