= Solution
Orthonormal <energy eigenstates> contribute incoherently to the expectation of <energy>:
$$
\langle E\rangle=
\frac{\epsilon}{S}\left[1(0.2)^2+4(0.3)^2+9(0.4)^2+16(0.843)^2\right]
=\frac{13.210384}{1.000649}\epsilon.
$$
Therefore \b[$\langle E\rangle\simeq13.2018\epsilon$] for the normalized literal decimals. Ignoring the small rounding-induced norm error gives $13.2104\epsilon$, conventionally reported at this precision as about \b[$13.2\epsilon$]. The mean need not equal an individual <energy> <eigenvalue>.
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