Suppose a simple random sample (X, i.i.d. observations) of size n is to be taken from a Normal distribution with both parameters u and o? are unknown. Let 0 = o? be the parameter of interest. Let ô = c E1 (X, – X)² denote the estimator of 0 = o? for a specified c > 0 where c depends on n. Answer the following: a) If n = 46, Ö, is unbiased, and Var(é.) = kot then k = b) If n = 28, 6, is the MLE, and Var(6) = kot then k = c) If n = 30, 6, is the MLE, and MSE(ê,, 0) = k oʻ then k = d) If n = 13, and é, has the smallest MSE then c = Note: Use at least 4 decimal places (rounded) in all the intermediate computations and in the answer submissions.

Suppose a simple random sample (X, i.i.d. observations) of size n is to be taken from a Normal distribution with both parameters u and o? are unknown. Let 0 = o? be the parameter of interest. Let ô = c E1 (X, – X)² denote the estimator of 0 = o? for a specified c > 0 where c depends on n. Answer the following: a) If n = 46, Ö, is unbiased, and Var(é.) = kot then k = b) If n = 28, 6, is the MLE, and Var(6) = kot then k = c) If n = 30, 6, is the MLE, and MSE(ê,, 0) = k oʻ then k = d) If n = 13, and é, has the smallest MSE then c = Note: Use at least 4 decimal places (rounded) in all the intermediate computations and in the answer submissions.

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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Suppose a simple random sample (X, i.i.d. observations) of size n is to be taken from a Normal distribution
with both parameters u and o? are unknown. Let 0 = o² be the parameter of interest.
Let ô = c E-1 (X; – X)² denote the estimator of 0 = o? for a specified c > 0 where c depends on n.
Answer the following:
a) If n = 46, Ö, is unbiased, and Var(é.) = k oʻ then k =
%3D
b) If n = 28, ô, is the MLE, and Var(6.) = k oʻ then k =
c) If n = 30, 6, is the MLE, and MSE(ê, 0) = k oʻ then k =
d) If n = 13, and 0, has the smallest MSE then c =
Note: Use at least 4 decimal places (rounded) in all the intermediate computations and in the answer
submissions.

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