Calculating the Mean Value of Vector n_i*n_j in 3D Space - Help and Explanation

Click For Summary

Homework Help Overview

The problem involves calculating the mean value of the product of components of a random unit vector in three-dimensional space, specifically focusing on the expression . The subject area pertains to vector mathematics and statistical expectations.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster seeks to understand the expectation value of the product of vector components. Some participants question the reasoning behind interpreting the mean value as a tensor of size 3x3, while others emphasize the need for showing work to support claims.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. There is a call for more detailed reasoning and clarification of concepts, indicating a productive exchange of ideas without a clear consensus yet.

Contextual Notes

Participants are encouraged to provide their reasoning and show work, which suggests a focus on understanding the underlying concepts rather than jumping to conclusions.

begyu85
Messages
5
Reaction score
0
vector mean value - help!

Homework Statement



Let n = (n_1, n_2, n_3) be a random unit vector in Descartes coordinates in the 3-dimensional space.

What is the mean value (or expectation value) of n_i*n_j, where i,j = 1,2,3.

Or shortly: < n_i*n_j > = ?
 
Physics news on Phys.org
Welcome To Pf.

Pls Show Some Work.
 
i think, this mean value is a tensor of 3x3
 
Why do you think that? You still haven't shown any work.
 

Similar threads

Graduate Hard-Core Boson Model in K space
  • · Replies 0 ·
Replies
0
Views
2K
The expected value for 7 heads in a row
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Sum principle proof: discrete mathematics
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Chunks of action smaller than Planck's constant
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad About the maximal extension of local charts on a manifold
  • · Replies 8 ·
Replies
8
Views
2K
What's the standard deviation of values in the histogram bar
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Hubbard model diagonalization in 1D K-space for spinless Fermions
  • · Replies 1 ·
Replies
1
Views
2K
How Do Primary Ideals in a PID Relate to Their Product and Intersection?
  • · Replies 1 ·
Replies
1
Views
2K
Non Existence An argument involving well-orders
  • · Replies 9 ·
Replies
9
Views
3K
3-D vectors forces exerted upon a mast
  • · Replies 7 ·
Replies
7
Views
2K