(6-14)  Continuing with our example from the previous question, we have a superposition state, created as a combination of the n=1 and n=2 states of our particle in a box: 

We interpret this as meaning that whenever a system is in this state and we make a measurement, so that the wavefunction collapses, the probability of ending up in a given eigenstate being determined by the square of its coefficient in this expression.

①  Because it must end up in one of the eigenstates, the sum of the coefficients in the superposition wavefunction must add up to 1. Confirm that this is so. 

②  The expectation value of the energy measured for a particle in state ys is written <E>.  This is the mean that would be measured for a very large number of such measurements for particles in this state. Write down an expression for the value of <E>.