Holding rate and clock fixed, longer recovery lowers the count. 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-second dead time gives ten counts

With 1 second dead time, the 15 second clock accepts 10 counts.

τ=1 s,N=10\tau=1\ \text{s},\quad N=10
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

Two-second dead time gives six counts

With 2 seconds dead time, the same clock accepts 6 counts, using 12 seconds dead.

τ=2 s,N=6,Td=12 s\tau=2\ \text{s},\quad N=6,\quad T_d=12\ \text{s}
Dead-time budgetDetected counts reserve dead-time intervals.clock=15 slive=3 srate=2 HzclockTime=15 sdeadTimeEach=2 sdetectedCount=6 countdeadTimeTotal=12 sliveTime=3 sobservedRate=2/5 Hz