Solution to Random Walk Problem | n_i

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Homework Help Overview

The discussion revolves around a random walk problem, specifically focusing on the notation ##n_i##, which represents the number of steps in the ith trial. Participants are attempting to understand the implications of this notation and how it relates to the overall problem of calculating the root mean square distance from the starting point after a series of steps.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning the meaning of ##n_i## and its role in the context of the random walk. There are attempts to derive an expression for the root mean square distance, with some participants expressing confusion about the necessary components, such as probabilities, in the calculations.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some have made attempts to formulate expressions related to the random walk, while others are seeking clarification on the inclusion of probabilities in their calculations. There is no explicit consensus yet, but guidance has been offered regarding the need for probabilities.

Contextual Notes

Participants are working under the constraints of a homework problem, which may limit the information available for discussion. The need for clarity on the definitions and relationships between the variables involved is evident.

arcTomato
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Homework Statement
Prove that the root mean square deviation for a walk involving the sum of different numbers n of steps of length λ
Relevant Equations
random walk
246472

I don't have any idea to prove this 😢
##n_i##is number of trial, right?
 
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arcTomato said:
##n_i##is number of trial, right?
##n_i## is the number of steps in the ith trial
 
I got it.
So,I think (4-12)means ##σ=Σ_in_iλ_i^2##, but I don't understand what is this 😢
 
arcTomato said:
I got it.
So,I think (4-12)means ##σ=Σ_in_iλ_i^2##, but I don't understand what is this 😢
You need to start from the other end.
You have a random walk in which n1 steps are of length λ1, n2 steps are of length λ2, and so on. I presume you are to take these as all being in the same straight line.
At the end of this walk you are at distance X from where you started. Can you write an expression for σ, the root mean square of X?
 
haruspex said:
Can you write an expression for σ, the root mean square of X?
uhh, I don't know how.
##σ^2=<X^2>=<(n_1λ_1+n_2λ_2+,,,,,n_iλ_i)^2>=<(n_1λ_1)^2>+<(n_2λ_2)^2>+,,,,,,##
like this??
 
arcTomato said:
uhh, I don't know how.
##σ^2=<X^2>=<(n_1λ_1+n_2λ_2+,,,,,n_iλ_i)^2>=<(n_1λ_1)^2>+<(n_2λ_2)^2>+,,,,,,##
like this??
No, you need some probabilities in there. Each step can be either way.
 
probabilities??like this??
246487
 

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