## Question

###### Let XiXn be an ii.d. sample from distribution with density function f(c; 0) = %r20-se-*/ , for â‚¬ > 0. Hint: Using wolfram alpha, E(X) = 38 and E(X? _ 1202 1. (Spts) Differentiate the log-likelihood function to find the score; and the MLE for &.2. (Zpts) Calculate the variance of the score function to get the Fisher information In (0) and the Cramer-Rao lower bound. 3. (Spts) Calculate the expected value and variance of the MLE: Based on that; is the MLE an efficient estimator?

Let Xi Xn be an ii.d. sample from distribution with density function f(c; 0) = %r20-se-*/ , for â‚¬ > 0. Hint: Using wolfram alpha, E(X) = 38 and E(X? _ 1202 1. (Spts) Differentiate the log-likelihood function to find the score; and the MLE for &. 2. (Zpts) Calculate the variance of the score function to get the Fisher information In (0) and the Cramer-Rao lower bound. 3. (Spts) Calculate the expected value and variance of the MLE: Based on that; is the MLE an efficient estimator?

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