1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Stats/thermal question

  1. Jan 26, 2006 #1
    Random walk in one dimension. A person (say, in an unstable state of mind/body) is moving in
    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?
    Last edited: Jan 26, 2006
  2. jcsd
  3. Jan 26, 2006 #2


    User Avatar
    Science Advisor

    Well, the way you set it up (if you're sure that's what the question is asking) that is just the mean of a binomial distribution with parameters N and p.
  4. Jan 26, 2006 #3
    ya i know, i used the binomial distribution formula to come up with that formula. I think thats the best i can do. I have a better question. What is the limit as n approaches infinity? Because one of the other questions asks what the large N limit is for the ratio Var(nR) / <nR> . I managed to derive the formula for Var(nR) to be p*d/dp(<nR>) - <nR>^2 , so the limit im looking for is (p*d/dp(<nR>))<nR> - <nR> , so as a start I would like to find the limit for large N of this <nR>. Anyone?
  5. Jan 26, 2006 #4
    my guess is p * N but how do i derive that mathematically?
  6. Jan 26, 2006 #5
    actually i think i messed up on the d/dp part, forgot to take into account that 1-p depends on p! If anyone can help me figure out a nice formula for the variance that would be great.
  7. Jan 26, 2006 #6


    User Avatar
    Science Advisor

    Well, it is p * N and the variance is Np(1 - p). John E. Freund's Mathematical Statistics gives proofs, but your book also probably does that. Never mind; I withdraw from this.
    Last edited: Jan 26, 2006
  8. Jan 27, 2006 #7
    Ya thanks, i was looking through my stats notes and saw the derivations. Im gonna try finishing up the other problems now. Assignment is due in the morning!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Stats/thermal question
  1. Stats Related Question (Replies: 1)

  2. Stats question (Replies: 4)

  3. Quick Stats question (Replies: 5)