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

AI Thread Summary
The discussion centers on calculating the mean value of the product of components of a random unit vector n in 3D space, specifically < n_i*n_j > for i, j = 1, 2, 3. Participants agree that this mean value results in a 3x3 tensor, as it represents the correlation between the vector components. There is a request for clarification and demonstration of the calculations involved. The conversation emphasizes the need for a detailed explanation and mathematical work to support the conclusion. Overall, the focus is on understanding the statistical properties of random unit vectors in three dimensions.
begyu85
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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 > = ?
 
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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.
 

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