# Standard deviation

Consider the Uniform distribution (continuous) U(-1,1) which has p.d.f. f(x) = 1/2 for -1 < x < 1 and 0 otherwise.

I have calculated the Fourier transform using the characteristic function and got fhat(epsilon)= sin(epsilon)/epsilon

How do I calculate the standard deviation of this distribution using both the Fourier transform and the definition. I know that the standard deviation is 1/sqrt(3) but how do I get this using whats above.