Question: Problem with calculating standard deviation symbolically

I am calculating the standard deviation of an function with StandardDeviation command both symbolically and numerically and I get different result for the symbolic and numeric calculation. The result of the symbolic calculation is wrong. Here is my problem: restart;with(Statistics): X := RandomVariable(Uniform(-Pi, Pi)); f:=1/abs(1-0.5*exp(-I*X)); StandardDeviation(f); # It gives 0, which is wrong. StandardDeviation(f, numeric); Re(%); Any idea?
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