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let X1,..., Xn be i.i.d. random variables with distribution N(µ, o²), with both u and o? unknown. (a). Show that the MLES of µ and o² are E(X; – X)² - ÎMLE = X = L=1 X; MLE n 1.:

let X1,..., Xn be i.i.d. random variables with distribution N(µ, o²), with both u and o? unknown. (a). Show that the MLES of µ and o² are E(X; – X)² - ÎMLE = X = L=1 X; MLE n 1.:

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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1. let X1,..., Xn be i.i.d. random variables with distribution N(u, o?), with both u and o? unknown. (a). Show that the MLES of u and o? are E(X; – X)? i=1 ÎMLE = X MLE n (b). Show that îûMLE is an unbiased estimator of mean, and derive its sampling distribution. (c). Show that ÔRLE is a biased estimator of variance. (d). If S2: E (X;-X)² show u^/s is tn-1 distribution. п-1 Hint: (n – 1)S = (n – 2)S-, + ("1) (X, – Xp-1)² п—1 In is independent of S
Transcribed Image Text:1. let X1,..., Xn be i.i.d. random variables with distribution N(u, o?), with both u and o? unknown. (a). Show that the MLES of u and o? are E(X; – X)? i=1 ÎMLE = X MLE n (b). Show that îûMLE is an unbiased estimator of mean, and derive its sampling distribution. (c). Show that ÔRLE is a biased estimator of variance. (d). If S2: E (X;-X)² show u^/s is tn-1 distribution. п-1 Hint: (n – 1)S = (n – 2)S-, + ("1) (X, – Xp-1)² п—1 In is independent of S
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