Random walk in one dimension. A person (say, in an unstable state of mind/body) is moving in(adsbygoogle = window.adsbygoogle || []).push({});

one dimension, with coordinate x, starting at x = 0. Assume: i.) that s/he moves in steps of length

l, ii.) that the probability that s/he takes a step to the left is p, while the probability of taking a

step to the right is q = 1 − p and iii.) that all the steps are independent (i.e. the probability of

taking the n + 1-th step left or right is independent on what the previous n steps were).

One of the questions ask: Find the average number of steps to the right, <nR>, taken after N steps.

This is what I got:

<nR> = sum i=0toN i*(N choose i) * p^(i) * (1-p)^(N-i)

A played around with it but i cant seem to get it into a nicer form. Other questions then ask for the variance and to compare it to the mean, so im sure i have to somehow eliminate the summation sign. There's a hint saying to use the fact that p d/dp(p^n) = np^n. Is there a way to simplify this?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Stats/thermal question

**Physics Forums | Science Articles, Homework Help, Discussion**