For the Laplace distribution f(x)=12be−∣x−μ∣bf(x) = \frac{1}{2b} e^{-\frac{|x-\mu|}{b}}f(x)=2b1e−b∣x−μ∣, what is the characteristic function ϕ(t)\phi(t)ϕ(t)?
eitμ1+b2t2\frac{e^{it\mu}}{1 + b^2t^2}1+b2t2eitμ
eitμ1−b2t2\frac{e^{it\mu}}{1 - b^2t^2}1−b2t2eitμ
11+b2t2\frac{1}{1 + b^2t^2}1+b2t21
eitμ−b∣t∣e^{it\mu - b|t|}eitμ−b∣t∣