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- Problem Statement
- prove that the mean position after a given number of steps is the starting position
- Relevant Equations
- random walk
I think I can prove equal length version problem, But I am confusing in this case,,,
Please help me!!
First things first. Make good on your "I think I can".....and show meProblem Statement: prove that the mean position after a given number of steps is the starting position
Relevant Equations: random walk
I think I can prove equal length version problem
First things first. Make good on your "I think I can".....and show me
Your formula for <k> is correct but how do I know it sums to zero?View attachment 246458
Is it wrong this photo??I thought this can prove equal length version.
If this is wrong, I have to withdraw my statement. ;;
Exactly. You would formally write that as##P(n,k)=P(-n,k)##
So, the pair of numerator are cancelled and the one having ##k=0## is uncancelled. this shows the sum is zero, right??
Why would you do this? The other result is two lines and it is patently correct. And the "fancy math" is the common language of probability which is the pedagogic purpose here.You don't need any fancy math.
Say you have two steps of different lengths x1 and x2. How about dividing each of those into smaller, equal-length steps of x0 each? So x1 + x2 = a*x0 + b*x0 where a and b are different positive integers. Now you have a series .of equal-length steps. And you know that equal-length steps of any number give a zero mean, right?
Absolutely.I think I got it
How can I write the calculation process???
##<k>=<k_0+k_1+k_2,,,,>=<k_0>+<k_1>+<k_2>+,,,,,=0##
right??
I don't see how that results in a proof. What is the mapping between this and the original problem? E.g. how does a sequence of n steps translate, and where might you end up?You don't need any fancy math.
Say you have two steps of different lengths x1 and x2. How about dividing each of those into smaller, equal-length steps of x0 each? So x1 + x2 = a*x0 + b*x0 where a and b are different positive integers. Now you have a series .of equal-length steps. And you know that equal-length steps of any number give a zero mean, right?