Show that The standard deviation is zero if and only if X is a constant function,that is ,X(s) = k for every s belonging to S,or ,simply X=k.
When they say constant function it means every element in S is been mapped to single element in the range.That is the single element is k.
Which means...
A point is chosen at random inside a circle.Find the probability 'p' that the point chosen is closer to the center of the circle than to its radius.
This comes from the noncountable uniform spaces sections.