a) Write down the log likelihood function for the sample and show that the MLE is the sample mean. b) Derive the score and the Hessian (it's a scalar here since there is only one parameter). Derive the information “matrix," which is scalar here. c) Derive the formulas for the Wald and LM tests of the hypothesis that 0= 0o (against the alternative that it's anything else). Verify that under the null the two test statistics have the same probability limit.

a) Write down the log likelihood function for the sample and show that the MLE is the sample mean. b) Derive the score and the Hessian (it's a scalar here since there is only one parameter). Derive the information “matrix," which is scalar here. c) Derive the formulas for the Wald and LM tests of the hypothesis that 0= 0o (against the alternative that it's anything else). Verify that under the null the two test statistics have the same probability limit.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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