Final answer:
The question asks for the normalization constant of a given wave function, which requires integrating the absolute square of the wave function over the specified domain and solving for A such that the total probability equals one.
Step-by-step explanation:
The student is asking for the normalization constant A for a particle's wave function that is given piecewise and also asks for certain probability measures and expectation values based on the given wave function. To find the normalization constant, one must ensure that the integral of the absolute square of the wave function over all space equals one. This condition stems from the probability interpretation of quantum mechanics stating that the total probability of finding a particle anywhere in space must be 100%. The correct approach involves computing the integral of the square of the function provided in the region where it is nonzero (from 0 to 3 in this case) and then solving for A to satisfy the normalization condition. Other parts of the question involve computing probabilities over specific intervals and quantum expectation values, requiring further integration and application of quantum mechanical operators.