Step unclear in Peebbles' Probability Book

In summary, the conversation discusses the process of going from line one of the autocorrelation to the second line, with one person struggling to understand the use of identity or property in the calculation. The other person suggests using the formula for the product of cosine values and apologizes for the delay in responding due to grad school. The struggling person expresses gratitude for the helpful suggestion.
  • #1
snatchingthepi
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TL;DR Summary
There's a step from one line to another that isn't clear to me.
If anyone could help me understand how Peebles gets from line one of the autocorrelation to the second line, I'd be most grateful. I don't understand what identity or property is being used to go from a product in the expectation value to a sum in the expectation value.
2019-11-23.png
 
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  • #2
I'm not sure I understand the step you are struggling with. Is it where they calculate ##R_{X,X}(t,t+\tau)##?

In that case, the formula

$$\cos(a) \cos(b)= 1/2(\cos(a+b)+\cos(a-b))$$ can be useful.
 
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  • #3
Sorry for the lateness of my thanks, but #gradschool. Yeah I feel slightly stupid now for not realizing that. It was exactly what I needed. Thank you.
 
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1. What is the main concept of "Step unclear in Peebbles' Probability Book"?

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The author of "Step unclear in Peebbles' Probability Book" is Professor Peebbles, a renowned expert in the field of probability and statistics. He has published numerous books and articles on the subject and has years of experience teaching at various universities.

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