## review derivation: variance relation

This page contains three views of the steps in the derivation: d3js, graphviz PNG, and a table.

Hold the mouse over a node to highlight that node and its neighbors. You can zoom in/out. You can pan the image. You can move nodes by clicking and dragging.

Notes for this derivation:

Options
Alternate views of this derivation:
Edit this content:

To edit a step, click on the number in the "Index" column in the table below

Clicking on the step index will take you to the page where you can edit that step.

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

$$x$$