Dead time and live time partition the observation clock. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Live time is the clock time left after dead time

The clock has 12 seconds, and dead time uses 8 seconds.

128=4 s12 - 8=4\ \text{s}
Dead-time budgetDetected counts reserve dead-time intervals.clock=12 slive=4 srate=2 HzclockTime=12 sdeadTimeEach=1 sdetectedCount=8 countdeadTimeTotal=8 sliveTime=4 sobservedRate=2/3 Hz

Only the remaining time can accept another pulse

The live remainder is 4 seconds.

Tlive=4 sT_{\text{live}}=4\ \text{s}
Dead-time budgetDetected counts reserve dead-time intervals.clock=12 slive=4 srate=2 HzclockTime=12 sdeadTimeEach=1 sdetectedCount=8 countdeadTimeTotal=8 sliveTime=4 sobservedRate=2/3 Hz