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5.5 Distribution of Time Intervals Between Counts

A distribution which we will make use of later is the distribution of time intervals between events from a random source. Suppose we observe a radioactive source with a mean rate lambda. The probability of observing no counts in a period T is then given by (57). In a manner similar to Section 5.4, we can interpret (57) as the probability density for the time interval T during which no counts are observed. Normalizing (57), we obtain the distribution

Equation 60 (60)

for the time T between counts. Equation (60) is just an exponential distribution and can, in fact, be measured.