Calculate L = E(Ä|X1) and find its variance. Is the variance of L smaller thanthe variance of X? Is L an estimator of X? Explain why this is. Consider a random sample X1,..., X, with n > 3 from the exponential distributionwith parameter 1 > 0 and densityf(x; A) = e-=/A,x > 0.Consider the following two estimators of A:3EXi, Ã =nX(1).i=1

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Answered: Calculate L = E(Ä|X1) and find its…

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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Psi is a measure of compressive strength, or the ability of the material to carry loads and handle compression. The desired concrete psi rating used for sidewalks and residential driveways ranges from 2500psi to 3000psi obtained from mixing cement, stone, and sand in different ratios but with the same amount of water. The summary of the psi's of three (3) such concrete mixes made by three (3) different civil engineering students is given as follows: Mean vector: The variance-covariance matrix: Concrete mix Mean Concrete mix 1 Concrete mix 2 Concrete mix 3 Concrete mix 1 | Concrete mix 2 2700 18 12 2 3000 12 16 3 2400 Concrete mix 3 16 25 Let the random variable Y be the vector of the psi's of concrete mixes obtained by the students, i.e. Y1, denotes the psi of concrete mix made by student 1, Y2 is the psi of concrete mix made by student 2 and Y3 is the psi of concrete mix psi made by student 3. (a) Find (i) the multivariate probability distribution function (pdf) of Y. (ii) the…
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Calculate L = E(Ä|X1) and find its variance. Is the variance of L smaller than the variance of Ä? Is L an estimator of X? Explain why this is.