Probability / Probability density

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SUMMARY

The discussion centers on the concept of probability density as explained in Feynman's Lectures, specifically section 6-4. It clarifies that for a particle moving in one dimension with an average step length of 1, the probability of the particle being at any specific distance from its starting position is zero due to the continuous nature of the probability distribution. This is because there are infinitely many possible step lengths, making the probability of any exact distance approach zero, or 1/infinity.

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Jelfish
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Quick question:

I just started reading Feynman's Lectures and in one section (6-4) he says that for a system in which a particle (in 1 dimension) can move in either direction (with equal prob. of either direction). For each 'step' that the particle takes, the distance it moves can be any length such that the average length is, say, 1, then the probability of the particle being any specific distance away from its starting position is zero.

Is this because there are theoretically an infinite number of lengths that the particle can step, and thus the probability for any specific distance approaches 1/infinity?

(note - I haven't taken any quantum physics classes yet, which I imagine is where this stuff may be taught)
 
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Your question is an elementary probability question (you don't need quantum physics). In the case described, the probability distribution is continuous, so that any specific value automatically has probability 0.
 
I'm sure I don't know enough about probability as I should. I realize that this doesn't rely on any quantum physics. I was just mentioning that it seems like something that would show up more often there. Just wanted to make sure I understood it correctly. Thanks for your response.
 

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