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review derivation: variance relation

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Index Inference Rule Input latex Feeds latex Output latex step validity dimension check unit check notes
1 declare identity
  1. 3585845894; locally 3493498:
    \(\langle \left(x-\langle x \rangle\right)^2 \rangle = \langle x^2 \rangle-\langle x \rangle^2\)
    \(pdg_{1464}\)
no validation is available for declarations 3585845894:
3585845894:
2 simplify
  1. 3585845894; locally 3493498:
    \(\langle \left(x-\langle x \rangle\right)^2 \rangle = \langle x^2 \rangle-\langle x \rangle^2\)
    \(pdg_{1464}\)
  1. 8399484849; locally 5049530:
    \(\langle x^2 - 2 x \langle x \rangle + \langle x \rangle^2 \rangle = \langle x^2 \rangle-\langle x \rangle^2\)
    \(pdg_{1464}\)
Nothing to split 3585845894:
8399484849:
3585845894:
8399484849:
3 simplify
  1. 8399484849; locally 5049530:
    \(\langle x^2 - 2 x \langle x \rangle + \langle x \rangle^2 \rangle = \langle x^2 \rangle-\langle x \rangle^2\)
    \(pdg_{1464}\)
  1. 2404934990; locally 6757584:
    \(\langle x^2\rangle -2\langle x \rangle\langle x \rangle+\langle x \rangle^2 = \langle x^2 \rangle-\langle x \rangle^2\)
    \(pdg_{1464}\)
Nothing to split 8399484849:
2404934990:
8399484849:
2404934990:
4 simplify
  1. 2404934990; locally 6757584:
    \(\langle x^2\rangle -2\langle x \rangle\langle x \rangle+\langle x \rangle^2 = \langle x^2 \rangle-\langle x \rangle^2\)
    \(pdg_{1464}\)
  1. 4949359835; locally 3294824:
    \(\langle x^2\rangle -2\langle x^2 \rangle+\langle x \rangle^2 = \langle x^2 \rangle-\langle x \rangle^2\)
    \(pdg_{1464}\)
Nothing to split 2404934990:
4949359835:
2404934990:
4949359835:
5 simplify
  1. 4949359835; locally 3294824:
    \(\langle x^2\rangle -2\langle x^2 \rangle+\langle x \rangle^2 = \langle x^2 \rangle-\langle x \rangle^2\)
    \(pdg_{1464}\)
  1. 2494533900; locally 5949484:
    \(\langle x^2\rangle -\langle x \rangle^2 = \langle x^2 \rangle-\langle x \rangle^2\)
    \(pdg_{1464}\)
Nothing to split 4949359835:
2494533900: no LHS/RHS split
 4949359835:
2494533900: N/A
6 claim LHS equals RHS
  1. 2494533900; locally 5949484:
    \(\langle x^2\rangle -\langle x \rangle^2 = \langle x^2 \rangle-\langle x \rangle^2\)
    \(pdg_{1464}\)
Nothing to split 2494533900: no LHS/RHS split
 2494533900: N/A
Physics Derivation Graph: Steps for variance relation

Symbols for this derivation

See also all 227 symbols
symbol ID category latex scope dimension name value Used in derivations references
1464 variable x
\(x\)		 ['real'] dimensionless 140
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