(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle moves in a sequence of steps of length L. The polar angle [tex]\theta[/tex] for each step is taken from the (normalized) probability density [tex]p(\theta)[/tex]. The azimuthal angle is uniformly distributed. Suppose the particle makes N steps.

My question is how do I find the expectation value (say [tex]<z^2>[/tex] for example).

2. Relevant equations

Usually for a probability density p(x) we have

[tex]<x^m>=\int x^m p(x) dx[/tex].

3. The attempt at a solution

I think that I can get the values for one step. eg.

[tex]<z^2>=\int_0^\pi (Lcos(\theta))^2p(\theta)d\theta={L^{2}\over 2}[/tex]

Note: the density [tex]p(\theta)[/tex] is normalized.

I just don't know how to treat N steps. Do I just multiply the one-step result by N?

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# Homework Help: Expectation values

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