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

zibi
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Prove or disprove that function \phi(t)=\frac{1}{1+|t|} is charcteristic function of some random variable.
 
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Okay, let's start with the definition. What is a characteristic function of a random variable?
 
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.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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