The sample mean x bar is the maximum likelihood estimator, Ask an Expert

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The sample mean X bar is the maximum likelihood estimator of sigma if the underlying p.d.f is f(x;sigma) = ((1/sigma)e^(-x/sigma)), 0 0. For this distribution, E(X bar) = sigma and Var(X bar) = sigma^2/n where n is the sample size. Use the fact that X bar is the approximately N(sigma, sigma^2/n) to construct an approximate 95 percent confidence interval for sigma.

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