Let (left{X_{n}ight}_{n=1}^{infty}) be a sequence of independent and identically distributed random variables from a (operatorname{LAPlace}(theta, 1)) distribution.
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Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of independent and identically distributed random variables from a \(\operatorname{LAPlace}(\theta, 1)\) distribution. Let \(\hat{\theta}_{n}\) denote the sample mean and \(\tilde{\theta}_{n}\) denote the sample median computed on \(X_{1}, \ldots, X_{n}\). Compute \(\operatorname{ARE}\left(\hat{\theta}_{n}, \tilde{\theta}ight)\).
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