Accidental Coincidences
Statistical Analysis
By Steve Kliewer
2008 SCIPP Workshop
Conditions for a Coincidence
A
B1
w
B2
w
Given an event on Channel A,
any event on channel B from B1 to B2 (i.e. before or after up to w away),
will trigger a coincidence
when the gate has been set to w.
Typical Values:
RA = 10 kHz
RB = 10 kHz
Gate: w = 1 s = 10-6 s
In a 1 second interval:
# of counts on A
= NA = RA
= 103
# of counts on B
= NB = RB
= 103
# of gate windows
= NW = 1/w
= 106
The probability of an event on a channel is:
PA = PB1 = PB2 = NA / Nw = RA w = RB1 w = RB2 w
The probability of a random coincidence on both is:
PC = PA * (PB1 + PB2 ) = 2*RA * RB w2
The expected rate of coincidences is:
RC = PC * Nw = 2*RA * RB w
= 2* 103 * 103 * 10-6
= 2 Hz