202410031745
Status: #idea
Tags: #statistics #math #physics
# Variance can be thought of as a time-based property
Variance is usually thought of as a measure of uncertainty, but it can also be thought of as a time property of a system.
Imagine we have a Gaussian with mean $\mu$ and variance $\sigma^2$ representing the position of an electron. We can think of $\sigma^2$ as our uncertainty of the electron's position, *or* we can think of it in the following way:
If we allow time $t$ to approach $\infty$, then the electron will eventually occupy all permissible permissions with proportion of instance where it occupies those positions defined by $\mathcal{N}(\mu, \sigma^2)$. Hence, the variance defines the **number of times the electron will occupy a position as time goes to infinity**.
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