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?

There is a discontinuity at 0, but discont gives no answer: discont(1/sin(abs(x)),x); Any idea?

How can one solve this simple inequality with Maple? I've tried : solve(sin(x)>0,x); and Maple gives no solution.