Prove that, if two random variables (tilde{x}_{1}) and (tilde{x}_{2}) are normally distributed and have the same mean

Question:

Prove that, if two random variables $\tilde{x}_{1}$ and $\tilde{x}_{2}$ are normally distributed and have the same mean $\mu$, then $\tilde{x}_{1} \succeq_{\text {SSD }} \tilde{x}_{2}$ if and only if $\sigma^{2}\left(\tilde{x}_{1}\right) \leq \sigma^{2}\left(\tilde{x}_{2}\right)$.

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