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  • https://math.libretexts.org/Under_Construction/Purgatory/Remixer_University/Username%3A_ASCCC/Statistics%3A_UC_Davis/1%3A_Notes/1.13%3A_13_Characteristic_functions
    Note that this is the distribution of the exponential distribution after being ``symmetrized'' in either of two ways: (i) We showed that if X,Y\sim \textrm{Exp}(1) are independent then X-Y has...Note that this is the distribution of the exponential distribution after being ``symmetrized'' in either of two ways: (i) We showed that if X,Y\sim \textrm{Exp}(1) are independent then X-Y has density e^{-|x|}; (ii) alternatively, it is the distribution of an ``exponential variable with random sign'', namely \varepsilon\cdot X where X\sim \textrm{Exp}(1) and \varepsilon is a random sign (same as the coin flip distribution mentioned above) that is independent of X.

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