Let X have a Pareto distribution with an unknown parameter α and known parameter θ = 20. We estimate α via the method of maximum likelihood by analyzing data from the following sample of four observations: 12 15 17 19. (a) Calculate l′′(α), the second derivative of the loglikelihood function. (b) Calculate the mle of α and its associated Fisher information. (c) E

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Let X have a Pareto distribution with an unknown parameter α and known parameter θ = 20. We estimate α via the method of maximum likelihood by analyzing data from the following sample of four observations: 12 15 17 19. (a) Calculate l′′(α), the second derivative of the loglikelihood function. (b) Calculate the mle of α and its associated Fisher information. (c) Estimate the variance of the maximum likelihood estimator. (d) Estimate an approximate 95% confidence interval for α. (e) Estimate EX and an approximate 95% confidence interval for EX using Delta method.
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