The help says the argument can be an algebraic expression involving a random variable or data list, as I understood.
( I have Maple 10)
For example, this calculation can be performed, here a is a parameter and Maple gives an general solution, I think Maple uses the definition integral to calculate the Mean symbolically:
restart;with(Statistics):
Y := RandomVariable('Uniform'(1, 2)):
Mean(1/(Y+a));

The help says the argument can be an algebraic expression involving a random variable or data list, as I understood.
( I have Maple 10)
For example, this calculation can be performed, here a is a parameter and Maple gives an general solution, I think Maple uses the definition integral to calculate the Mean symbolically:
restart;with(Statistics):
Y := RandomVariable('Uniform'(1, 2)):
Mean(1/(Y+a));

First, I tried that without any success:
restart;
with(Statistics):
X:=RandomVariable(Uniform(-Pi,Pi));
f:= 1/ abs(1-Gt*Gr*exp(-I*X));
assume(Gt::RealRange(Open(0),Open(1)),Gr::RealRange(Open(0),Open(1)));
about(Gt);about(Gr);
StandardDeviation(f);
# and I just tried to calculate Mean, but it gives me -1, which
#is incorrect. !
Mean(f);

First, I tried that without any success:
restart;
with(Statistics):
X:=RandomVariable(Uniform(-Pi,Pi));
f:= 1/ abs(1-Gt*Gr*exp(-I*X));
assume(Gt::RealRange(Open(0),Open(1)),Gr::RealRange(Open(0),Open(1)));
about(Gt);about(Gr);
StandardDeviation(f);
# and I just tried to calculate Mean, but it gives me -1, which
#is incorrect. !
Mean(f);

Thanks for your comment.
The value of f is real, because of abs.
Doesn't this phrase in the help refer to data list/set input only? In this case I have an expression.
Perhaps is this an integration problem?
Originally I wanted to calculate of the standard deviation of this expression:
f:= 1/ abs(1-Gt*Gr*exp(-I*phi);
where Gt and Gr are real constants, its values between 0 and 1 (open range), and phi is a random variable of uniform distribution, between -Pi and Pi.
The calculation failed, then I tried to solve the simplified problem.

Thanks for your comment.
The value of f is real, because of abs.
Doesn't this phrase in the help refer to data list/set input only? In this case I have an expression.
Perhaps is this an integration problem?
Originally I wanted to calculate of the standard deviation of this expression:
f:= 1/ abs(1-Gt*Gr*exp(-I*phi);
where Gt and Gr are real constants, its values between 0 and 1 (open range), and phi is a random variable of uniform distribution, between -Pi and Pi.
The calculation failed, then I tried to solve the simplified problem.

Thank you for your comment.
I hope this bug will be fixed.

Thank you for your comment.
I hope this bug will be fixed.

Thank you for your answer.
Shouldn't the FunctionAdvisor database contain much more information about the sin and other elementary/special functions (where the elementary function is positive etc. )? Perhaps such problems could be easily solved by Maple.

Thank you for your answer.
Shouldn't the FunctionAdvisor database contain much more information about the sin and other elementary/special functions (where the elementary function is positive etc. )? Perhaps such problems could be easily solved by Maple.

Thank you for your answer.
Of course, there are infinitely number of solutions.
As far as I know Maple can handle with infinitely number of solutions of an equation, but it seems, it is not true for the inequalities or inequalities with special functions. (Of course I tried the _EnvAllSolutions option of solve etc.)
I tried to restrict the x for an interval of sin, but it gives no one interval of the solutions.

Thank you for your answer.
Of course, there are infinitely number of solutions.
As far as I know Maple can handle with infinitely number of solutions of an equation, but it seems, it is not true for the inequalities or inequalities with special functions. (Of course I tried the _EnvAllSolutions option of solve etc.)
I tried to restrict the x for an interval of sin, but it gives no one interval of the solutions.