Average Energy Is a Weighted Ledger - Statistical Physics: Ensembles, Weights, and Fluctuations Step by Step

The average energy is a source-bound weighted sum. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Average energy uses the weighted numerator

The checked numerator is eight joules.

E_{\rm num}=8\ {\rm J}

The average divides by the partition total

The average energy is eight sevenths of a joule.

\langle E\rangle=\frac{8}{7}\ {\rm J}