Qs. A random sample X1, X2, ..., Xn is drawn from a Pareto population with pdf f(r; 0, v) = „0+1»* 2 v,0 > 0, v > 0. (a) Find the MLE of 0 and v. (b) Perform a LRT of Ho : 0 = 1, v is unknown, versus H1 : 0 + 1, v is unknown. Show that the critical region of the test is of the form {T(x) < cı or T(x) > c2}, where 0 < c1 < c2 and II-, X; (min X;)" T = log (c) Show that, under Ho, 2T has a chi-squared distribution, and find its degrees of freedom.

Qs. A random sample X1, X2, ..., Xn is drawn from a Pareto population with pdf f(r; 0, v) = „0+1»* 2 v,0 > 0, v > 0. (a) Find the MLE of 0 and v. (b) Perform a LRT of Ho : 0 = 1, v is unknown, versus H1 : 0 + 1, v is unknown. Show that the critical region of the test is of the form {T(x) < cı or T(x) > c2}, where 0 < c1 < c2 and II-, X; (min X;)" T = log (c) Show that, under Ho, 2T has a chi-squared distribution, and find its degrees of freedom.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
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