Answer to Question #60651 in Statistics and Probability for esita

Question

8. a) Show that ∑=
=
n
i
n
n
x
X
1
, in random sampling from





− θ < < ∞
θ = θ
;0 elsewhere
exp( / ); 0
1
( , )
x x
f x
where 0 < θ < ∞ , is an MVB estimator of θ and has variance / n
2
θ . (4)
b) Find the maximum likelihood estimator for the parameter λ of a Poisson distribution
on the basis of a sample of size n . Also find its variance. (3)
c) Given one observation from a population with p.d.f.:
θ − ≤ ≤ θ
θ
f x θ = ( x); 0 x
2
( , )
2
Obtain )% 100 1( −α confidence interval for θ .