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.