Answered: A statistician has to decide on the…

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

A statistician has to decide on the basis of two obser-
vations whether the parameter θ of a binomial distribu-
tion is 1

4 or 1
2 ; his loss (a penalty that is deducted from his
fee) is $160 if he is wrong.
(a) Construct a table showing the four possible values of
the loss function.

(b) List the eight possible decision functions and con-
struct a table showing all the values of the corresponding

risk function.
(c) Show that three of the decision functions are not
admissible.
(d) Find the decision function that is best according to the
minimax criterion.
(e) Find the decision function that is best according to the
Bayes criterion if the probabilities assigned to θ = 1
4 and

θ = 1
2 are, respectively, 2
3 and 1
3 .

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