elsewhere i) Show that f(x; 0) 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 6 = ₁X₁ is the maximum likelihood estimator of the parameter 0. :1 iii) Is the maximum likelihood estimator = 1X₁, an efficient estimator of ? 1n n

MATLAB: An Introduction with Applications
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b) Suppose that a sequence of mutually independent and identically distributed continuous
random variables X₁, X₂, X3,..., Xn has the probability density function
1 (x-0)²
2
f(x; 0) =
∞<x< 00
√2π
0
elsewhere
i) Show that f(x; 0) belongs to the one-parameter regular exponential family. Clearly
indicate the following functions, h(x), c(0), w(0) and t(x).
1m
ii) Show that Ô===₁ X₁ is the maximum likelihood estimator of the parameter 0.
=1
e
for
iii) Is the maximum likelihood estimator == ₁ X₁, an efficient estimator of 0?
i=1
n
Transcribed Image Text:b) Suppose that a sequence of mutually independent and identically distributed continuous random variables X₁, X₂, X3,..., Xn has the probability density function 1 (x-0)² 2 f(x; 0) = ∞<x< 00 √2π 0 elsewhere i) Show that f(x; 0) belongs to the one-parameter regular exponential family. Clearly indicate the following functions, h(x), c(0), w(0) and t(x). 1m ii) Show that Ô===₁ X₁ is the maximum likelihood estimator of the parameter 0. =1 e for iii) Is the maximum likelihood estimator == ₁ X₁, an efficient estimator of 0? i=1 n
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