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Finally, since f (l) is a probability density, its integral must be equal to 1 so that we can think of the gamma function as a normalization constant, as in J0°°f (1)d1 = 1 from which we conclude a—ali v—1

Thus, the right hand integral in Eq. (3.55) allows us to see that a2 iv— l e—a22v—M2 = r(v)/av which will be very handy when we find the mean and variance of the encounter rate. Note that we have just taken advantage of the information that f (2) is a probability density to do what appears to be a very difficult integral in our heads ! Richard Feynman claimed that this trick was very effective at helping him impress young women in the 1940s (Feynman 1985).

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