3.3.2 Statistics of quantum operators

1

If the wave function of a one dimensional harmonic oscillator is

$$\sqrt{\frac{1}{2}}\psi_0 + \sqrt{\frac{1}{2}}\psi_1 + 0 \psi_2$$

where the eigenfunctions have energies $\frac12\hbar\omega$, $\frac32\hbar\omega$, and $\frac52\hbar\omega$, then what is the expectation value of the energy?