Consider the density 1+ ax f (x; a) ,-1< x <1 and 2 -1< a< 1, where x = cos 0. Suppose we have an iid sample X1,..., X,n from f(x;a). (a). Find the method of moments estimator â of a and show that it is unbiased. (b) Find the variance of â, Var(â). Use the Central Limit Theorem to deduce a Normal approximation to the sampling (c)- distribution of â. If n = 25 and a = 0, what is the P(|â| > 0.5)?
Consider the density 1+ ax f (x; a) ,-1< x <1 and 2 -1< a< 1, where x = cos 0. Suppose we have an iid sample X1,..., X,n from f(x;a). (a). Find the method of moments estimator â of a and show that it is unbiased. (b) Find the variance of â, Var(â). Use the Central Limit Theorem to deduce a Normal approximation to the sampling (c)- distribution of â. If n = 25 and a = 0, what is the P(|â| > 0.5)?
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
![Consider the density
1+ ax
f (x; a) =
-1< x <1 and
-1<α< 1,
where x = cos 0. Suppose we have an iid sample X1,..., Xn from f(x; a).
(a).
Find the method of moments estimator â of a and show that it is unbiased.
(b)
Find the variance of â, Var(â).
Use the Central Limit Theorem to deduce a Normal approximation to the sampling
(c)-
distribution of â. If n = 25 and a = 0, what is the P(lâ| > 0.5)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34934fde-95ac-45f2-b559-2afabddf17db%2Fb52a2c96-c1c0-4886-9651-bccfbb492452%2F1ebl2dh_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the density
1+ ax
f (x; a) =
-1< x <1 and
-1<α< 1,
where x = cos 0. Suppose we have an iid sample X1,..., Xn from f(x; a).
(a).
Find the method of moments estimator â of a and show that it is unbiased.
(b)
Find the variance of â, Var(â).
Use the Central Limit Theorem to deduce a Normal approximation to the sampling
(c)-
distribution of â. If n = 25 and a = 0, what is the P(lâ| > 0.5)?
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