Let (tilde{x}_{1}) be a random variable taking values ({-1,1,0}) with probabilities ({pi, pi, 1-2 pi}), respectively, and

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Let \(\tilde{x}_{1}\) be a random variable taking values \(\{-1,1,0\}\) with probabilities \(\{\pi, \pi, 1-2 \pi\}\), respectively, and \(\tilde{x}_{2}\) a random variable taking values \(\{-1,1,0\}\) with probabilities \(\{\gamma, \gamma, 1-2 \gamma\}\), respectively. Show that \(\tilde{x}_{1} \succeq_{\text {SSD }} \tilde{x}_{2}\) if and only if \(\gamma \geq \pi\).

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