Particle Moving between Two Barriers 

The collision times for a particle moving between two barriers are distributed exponentially, with a mean of three microseconds. If the particle starts at the right-hand barrier () and moves towards the left-hand barrier (), then simulate the collision process for 100 microseconds.

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X collisionProcess = TelegraphProcess[1/3];

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X sample = RandomFunction[collisionProcess, {0, 100}];

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X ListLinePlot[sample["Path"], InterpolationOrder -> 0, Filling -> Axis]

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Variance for the slice distribution is 1.

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X Variance[collisionProcess[100]]

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Compare with the variance of a sample.

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X Variance[RandomVariate[collisionProcess[100], 10^4]] // N

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