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The random variables X, X2,..., Xn are independent and identically distributed random vari- ables with common probability density function (pdf) Sx (=) = { o, z4 (0,1). y?-1, x € (0, 1), x¢ (0, 1), fx (x) = { where y 0

The random variables X, X2,..., Xn are independent and identically distributed random vari- ables with common probability density function (pdf) Sx (=) = { o, z4 (0,1). y?-1, x € (0, 1), x¢ (0, 1), fx (x) = { where y 0

MATLAB: An Introduction with Applications
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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Question 2 ( The random variables X, X2,..., Xn are independent and identically distributed random vari- ables with common probability density function (pdf) fx (x) = { v, x € (0, 1), 0, x ¢ (0, 1), where y> 0. Note: You may use the fact that - log X;, i = 1, ...,n, follow an exponential distribution with mean 1/y. (a) Show that - , log , is a sufficient statistic for y. (b) Show that -yElog X; is a pivotal quantity and that a 100(1-a)% confidence interval for y is of the form a E log X;' - , log X: where a and b are some constants.
Transcribed Image Text:Question 2 ( The random variables X, X2,..., Xn are independent and identically distributed random vari- ables with common probability density function (pdf) fx (x) = { v, x € (0, 1), 0, x ¢ (0, 1), where y> 0. Note: You may use the fact that - log X;, i = 1, ...,n, follow an exponential distribution with mean 1/y. (a) Show that - , log , is a sufficient statistic for y. (b) Show that -yElog X; is a pivotal quantity and that a 100(1-a)% confidence interval for y is of the form a E log X;' - , log X: where a and b are some constants.
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