Suppose that a sequence of mutually independent and identically distributed discrete randomvariables X₁, X₂, X3, ..., Xn has the following probability density function0xe-0x!0,a)b)c)f(x; 0) =for x = 0,1,2,...elsewhere1 nShow that for any & > 0 and S₂ = ₁X₁, lim P(|S, − 0| ≥ ɛ) = 0.-Zi=1nn→∞Show that a statistic Sn in a) is the maximum likelihood estimator of the parameter 8.Let Ô₁ X₁+2X₂+2X3-X4=4¹ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Whichone of the two estimators is more efficient?

Given X~pois(θ) Mean=E(X)=V(X)=variance=θ X1, X2, ... Xn be the independent variables.

Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3, ..., Xn has the following probability density function 0xe-0 x! 0, a) b) c) f(x; 0) = for x = 0,1,2,... elsewhere Show that for any & > 0 and S₂ = ₁ X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. 1 n Zi=1 - n n-8 Show that a statistic Sn in a) is the maximum likelihood estimator of the parameter 8. Let Ô₁ X₁+2X₂+2X3-X4 = 4 ¹ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Which one of the two estimators is more efficient?

Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3, ..., Xn has the following probability density function 0xe-0 x! 0, a) b) c) f(x; 0) = for x = 0,1,2,... elsewhere Show that for any & > 0 and S₂ = ₁ X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. 1 n Zi=1 - n n-8 Show that a statistic Sn in a) is the maximum likelihood estimator of the parameter 8. Let Ô₁ X₁+2X₂+2X3-X4 = 4 ¹ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Which one of the two estimators is more efficient?

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

Suppose that a sequence of mutually independent and identically distributed discrete random
variables X₁, X₂, X3, ..., Xn has the following probability density function
0xe-0
x!
0,
a)
b)
c)
f(x; 0) =
for x = 0,1,2,...
elsewhere
1 n
Show that for any & > 0 and S₂ = ₁X₁, lim P(|S, − 0| ≥ ɛ) = 0.
-
Zi=1
n
n→∞
Show that a statistic Sn in a) is the maximum likelihood estimator of the parameter 8.
Let Ô₁ X₁+2X₂+2X3-X4
=
4
¹ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 8. Which
one of the two estimators is more efficient?

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Suppose that a sequence of mutually independent and identically distributed discrete random variables X₁, X₂, X3, ..., Xn has the following probability density function a) b) c) f(x; 0) = 0xe-0 x! 0, J for x = 0,1,2,... elsewhere Show that for any & > 0 and S₂ = = =₁ X₁, lim P(|S₂ − 0| ≥ ɛ) = 0. n n-00 one of the two estimators is more efficient? Show that a statistic S₁ in a) is the maximum likelihood estimator of the parameter 8. Let Ô₁ = X1+2X2+2X3-X4 4 ¹ and Ô₂ = ²(X₁ + X₂ + X3 + X4) be two unbiased estimators of 0. Which