b) Suppose that a sequence of mutually independent and identically distributed continuous random variables X₁ X₂ X3 X has the probability density function 1(x-8)² *** f(x; 6)=√√2 for-∞0
b) Suppose that a sequence of mutually independent and identically distributed continuous random variables X₁ X₂ X3 X has the probability density function 1(x-8)² *** f(x; 6)=√√2 for-∞0
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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Transcribed Image Text:b) Suppose that a sequence of mutually independent and identically distributed continuous
random variables X₁, X₂, X3,..., X has the probability density function
-√√2/²
i)
2 foro < x < 0⁰
elsewhere
Show that f(x; 6) belongs to the one-parameter regular exponential family. Clearly
indicate the following functions, h(x), c(0), w(0) and t(x).
ii) Show that 8=EX, is the maximum likelihood estimator of the parameter 0.
iii) is the maximum likelihood estimator 6=EX₁, an efficient estimator of 6?
_(x-0)²
f(x; 0)=√√√2
Transcribed Image Text:b) Suppose that a sequence of mutually independent and identically distributed continuous
random variables X₁, X₂, X3,..., X has the probability density function
-√√2+²
i)
2 foro < x < 0⁰
elsewhere
Show that f(x; 6) belongs to the one-parameter regular exponential family. Clearly
indicate the following functions, h(x), c(0), w(0) and t(x).
ii) Show that ΣX, is the maximum likelihood estimator of the parameter 0.
iii) is the maximum likelihood estimator 6=EX₁, an efficient estimator of 6?
_(x-0)²
f(x; 0)=√√√2
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