Ensemble Counts

Expected Counts Come from Fractions

Expected counts are checked integer products of population and probability. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Choose a finite population

A population of 40 makes both expected counts integers.

40 particles40\ \text{particles}
Ensemble weight ledgerFinite state weights produce exact probabilities and expected counts.probprobcountcount

Expected counts multiply probabilities

The expected counts are 10 and 30.

40⋅14=10,40⋅34=3040\cdot\frac{1}{4}=10,\quad40\cdot\frac{3}{4}=30
Ensemble weight ledgerFinite state weights produce exact probabilities and expected counts.probprobcountcount