Chance in Biology by Denny Mark;Gaines Steven;Gaines Steven;

Author:Denny, Mark;Gaines, Steven;Gaines, Steven; [Denny, Mark;Gaines, Steven;Gaines, Steven;]
Language: eng
Format: epub
ISBN: 0691005214
Publisher: Princeton UP
Published: 2011-09-15T05:00:00+00:00

FIG. 6.2 Diffusion to capture. The average time to capture varies depending on where a particle is released and whether the walls are absorbing or reflecting.

There are cases in which we will not know beforehand at what position a particle begins its walk. In this situation, it can be useful to calculate an overall average time to capture for particles that have an equal probability of starting anywhere on the axis (that is, a uniform distribution) between 0 and b. This is just the formula for the expected value of a continuous random variable, as described in chapter 4. Each position x has a value (x) and the probability density function for a uniform distribution (i.e., 1/b):

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