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