MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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3. Let X₁,..., Xn be a random sample from the normal N(μ, o²) distribution with mean µ and known variance o². Recall that the probability density function (PDF) of N(µ, o²) is given by fx (5:14,0²³) = √2/1072 Exp ((2-4)²), (x (x; 12πσ2 for -∞ < x <∞, μ E R, and σ > 0. (a) Write down the joint PDF of (X₁,. 2 Xn). Identify a sufficient statistic for µ.
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Transcribed Image Text:3. Let X₁,..., Xn be a random sample from the normal N(μ, o²) distribution with mean µ and known variance o². Recall that the probability density function (PDF) of N(µ, o²) is given by fx (5:14,0²³) = √2/1072 Exp ((2-4)²), (x (x; 12πσ2 for -∞ < x <∞, μ E R, and σ > 0. (a) Write down the joint PDF of (X₁,. 2 Xn). Identify a sufficient statistic for µ.
(b) Obtain the maximum likelihood estimator (MLE) μ of µ.
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Transcribed Image Text:(b) Obtain the maximum likelihood estimator (MLE) μ of µ.
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