A longer observation clock can contain more accepted counts and their recovery intervals when the rate and dead time stay fixed. The comparison is exact only for the stated clock durations, rate, and nonparalyzable rule; measured runs add live-time accounting error, source drift, missed pulses, and finite-count uncertainty.

A longer observation time can hold more recovery intervals. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A longer clock accepts more counts

Keeping rate 2 hertz and dead time 1 second, a 15 second clock gives 10 counts.

10(1+2×1)=2×1510( 1+2\times1 )=2\times15
Dead-time budgetDetected counts reserve dead-time intervals.clock=15 slive=5 srate=2 HzclockTime=15 sdeadTimeEach=1 sdetectedCount=10 countdeadTimeTotal=10 sliveTime=5 sobservedRate=2/3 Hz

The longer clock still keeps a dead/live budget

The 10 seconds of dead time leave 5 seconds live.

15−10=515 - 10=5
Dead-time budgetDetected counts reserve dead-time intervals.clock=15 slive=5 srate=2 HzclockTime=15 sdeadTimeEach=1 sdetectedCount=10 countdeadTimeTotal=10 sliveTime=5 sobservedRate=2/3 Hz