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Accidental Coincidences Statistical Analysis By Steve Kliewer 2008 SCIPP Workshop

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Conditions for a Coincidence A wB1B1 wB2B2 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.

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Typical Values: R A = 10 kHz R B = 10 kHz Gate: w = 1 s = 10 -6 s In a 1 second interval: # of counts on A = N A = R A = 10 3 # of counts on B = N B = R B = 10 3 # of gate windows = N W = 1/w = 10 6

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The probability of an event on a channel is: P A = P B1 = P B2 = N A / N w = R A w = R B1 w = R B2 w The probability of a random coincidence on both is: P C = P A * ( P B1 + P B2 ) = 2* R A * R B w 2 The expected rate of coincidences is: R C = P C * N w = 2* R A * R B w = 2* 10 3 * 10 3 * 10 -6 = 2 Hz

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