In the problems below we consider the following setup. Let X₁,..., Xn be independent copies of the random va where X is a mixture of two uniform random variables and has pdf:
In the problems below we consider the following setup. Let X₁,..., Xn be independent copies of the random va where X is a mixture of two uniform random variables and has pdf:
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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![5. Mixture of Uniforms
In the problems below we consider the following setup. Let X₁,..., Xn be independent copies of the random variable X
where X is a mixture of two uniform random variables and has pdf:
f (x) = 1/1(
40
1 (x = [0,20]) + ¹1 (x = [0,30])
40
for some unknown > 0. For this problem, we call Unif([0, 20], the first component.
Second Initialization: EM for a Uniform Mixture
Assume that n = 8 and the observations are
X₁ = 1.01 X₂ = 1.02 X3 = 1.19 X4
= 1.19
X5 1.28 X6 = 2.39 X7 = 2.56 X = 2.58
Assume that the EM algorithm is initialized at 00
1. What do the iterations of the EM algorithm converge to?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faaffd6db-862a-4938-a665-6b497e83668d%2F946eab65-1944-4427-af40-b0cf475b4c64%2Fe3x9t1m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Mixture of Uniforms
In the problems below we consider the following setup. Let X₁,..., Xn be independent copies of the random variable X
where X is a mixture of two uniform random variables and has pdf:
f (x) = 1/1(
40
1 (x = [0,20]) + ¹1 (x = [0,30])
40
for some unknown > 0. For this problem, we call Unif([0, 20], the first component.
Second Initialization: EM for a Uniform Mixture
Assume that n = 8 and the observations are
X₁ = 1.01 X₂ = 1.02 X3 = 1.19 X4
= 1.19
X5 1.28 X6 = 2.39 X7 = 2.56 X = 2.58
Assume that the EM algorithm is initialized at 00
1. What do the iterations of the EM algorithm converge to?
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