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Suppose that the counts recorded by a Geiger counter follow a Poisson process with an average...

Suppose that the counts recorded by a Geiger counter follow a Poisson process with an average of two counts per minute. What is the probability that the first count occurs between two and 3 minutes after start-up?

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Answer:

Calculate the probability that the first count occurs between 2 and 3 minutes after start-up.

Average of 2 counts per minute is same as waiting time of 0.5 minutes per count.

Let T be the time to get the first count (in min).

Here,

The distribution function for T is,

P(2<=T<=3) = P(T<=3) - P(T<=2)

=( 1 - e-3/0.5) - ( 1 - e-2/0.5) = 0.0183 - 0.0024788 = 0.01582

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