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\sect{Formula for the canonical fluctuations in energy}

Prove that  ${\sigma_{E}^{2}=T^{2}C_{X}}$

Where ${\sigma_{E}^{2}\equiv \langle H^{2}\rangle - \langle
H\rangle^{2}}$

and ${C_{X}\equiv \frac{\partial E}{\partial T}|_{X}}$

Guideline: Express ${\sigma_{E}^{2}}$ by the distribution function
and use the result we got for ${E}$ in order to get the requested
expression.


