1. Not finding help here? Sign up for a free 30min 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!

Probabilities: The mean of the square

  1. Jan 13, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    A particle can choose randomly to move in one of these directions:

    [tex]
    r_1 = (a,0), \quad r_2 = (-a,0), \quad r_3 = (0,a) \quad \text{and}\quad r_4 = (0,-a).
    [/tex]

    These are vectors, not coordinates! I have to find the mean of the square of r, i.e. [itex]<r>[/itex] after n moves, where the particle starts in (0,0).

    What I have done is the following:

    [tex]
    <r^2> = \sum_i {(r_i\cdot r_i)P_i},
    [/tex]

    where Pi is 1/4, because it is random. So I believe the mean of the square of r is a2. But my teacher says it is na2. I cannot see why he wants to multiply by n, since my method is quite straightforward. Where am I wrong?

    Thanks in advance.

    Best regards,
    Niles.
     
  2. jcsd
  3. Jan 13, 2009 #2
    You gotta have an n somewhere, otherwise, how do you incorporate the fact that it is after n moves? Your expression currently find mean of r^2 after the first step.

    For n moves, you'll have n terms and each step has a different possibility. You should think about how to arrive at the corresponding expression.










    Hint:
    [tex]\langle r^2 \rangle=\overbrace{\sum ... \sum}^{\rm{n times}}(r_1+r_2+...+r_n)^2 \times \rm{Probability}[/tex]

    Now, how would you simplify that?
     
  4. Jan 14, 2009 #3
    Thanks, I see it now.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?