Here's my understanding. Please let me know what I'm missing or what I've misunderstood. <x> represents the average of position measurements on some N, identically prepared particles. If those measurements are thought of as a distribution, then that distribution's form should match the wave...
The wave function described seems impossible. Wave functions have to be differentiable at all points, right? Otherwise they don't represent a physically realizable state. The wave function in the example isn't differentiable at x=A, the maximum point. Also, for problem (c), I know it's visually...