Partition Total Normalizes the Weights - Statistical Physics: Ensembles, Weights, and Fluctuations Step by Step

A finite weighted ensemble has one checked normalizing total. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

One partition total normalizes every row

The explicit weights add to seven.

Z=4+2+1=7

Each probability uses the same total

The three probabilities share that one total.

\frac{4}{7},\quad\frac{2}{7},\quad\frac{1}{7}