Write Proof "Derivation of the Akaike information criterion"

Corresponding Definition: ["Akaike information criterion"](https://statproofbook.github.io/D/aic).
Proof that could serve as inspiration: ["Derivation of the Bayesian information criterion"](https://statproofbook.github.io/P/bic-der).
Proof should be placed under this link: ["Derivation of the Akaike information criterion"](https://statproofbook.github.io/P/aic-der).