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7. (MOM, MLE, FI, DM) Let X1, X2,..., Xn be a random sample of Beta(1,0) random variables. The density function fx(x) = c(0)(1-x)-1, 0x1,
7. (MOM, MLE, FI, DM) Let X1, X2,..., Xn be a random sample of Beta(1,0) random variables. The density function fx(x) = c(0)(1-x)-1, 0x1, 0>0. (a) Find the value of c(0) so that fx (2|0) is a density function. (b) Find the maximum likelihood estimator for 0. (c) Find the method of moments estimator of 0. (d) Use the delta method to estimate the standard deviations of the two estimators. (e) Find the Fisher information. How do the standard deviation estimates in the previous part relate to the Fisher information?
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Probability And Statistics For Engineering And The Sciences
Authors: Jay L. Devore
9th Edition
1305251806, 978-1305251809
