Is \(\phi(t) = \frac{1}{1+|t|}\) a Characteristic Function of a Random Variable?

[zibi]

Prove or disprove that function $$\phi(t)=\frac{1}{1+|t|}$$ is charcteristic function of some random variable.

 

[HallsofIvy]

Okay, let's start with the definition. What is a characteristic function of a random variable?

 

[zibi]

you are proposing to apply inverse Fourier transform and to check whether the function we will get can be density function ? So how can inverse Fourier transform be computed in this case ? that's my question now.