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: for some unknown > 0. For this problem, we call Unif([0, 20], the first component. First Initialization: EM for a Uniform Mixture Assume that n = 8 and the observations are 5. Mixture of Uniforms 0₁ ƒ (x) = 1 (x = [0, 20]) + 11 (x = [0,30)) 40 40 0₂ 03 Assume that the EM algorithm is initialized at 00 = 3. What are the values of the first three iterates 01, 02, and 03 of the EM algorithm? || X₁ = 1.01 X₂ = 1.02 X3 = 1.19 X₁ 1.19 X5 1.28 X6 = 2.39 X7 = 2.56 X = 2.58
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: for some unknown > 0. For this problem, we call Unif([0, 20], the first component. First Initialization: EM for a Uniform Mixture Assume that n = 8 and the observations are 5. Mixture of Uniforms 0₁ ƒ (x) = 1 (x = [0, 20]) + 11 (x = [0,30)) 40 40 0₂ 03 Assume that the EM algorithm is initialized at 00 = 3. What are the values of the first three iterates 01, 02, and 03 of the EM algorithm? || X₁ = 1.01 X₂ = 1.02 X3 = 1.19 X₁ 1.19 X5 1.28 X6 = 2.39 X7 = 2.56 X = 2.58
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![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:
for some unknown > 0. For this problem, we call Unif([0, 20], the first component.
First Initialization: EM for a Uniform Mixture
Assume that n = 8 and the observations are
5. Mixture of Uniforms
0₁
ƒ (x) = 1 (x = [0, 20]) + 11 (x = [0,30))
40
40
0₂
03
Assume that the EM algorithm is initialized at 00 = 3. What are the values of the first three iterates 01, 02, and 03 of the EM
algorithm?
||
X₁ = 1.01 X₂ = 1.02 X3 = 1.19 X₁ 1.19
X5 1.28 X6 = 2.39 X7 = 2.56 X = 2.58](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faaffd6db-862a-4938-a665-6b497e83668d%2F37ba110f-10ed-45bb-b58c-21d2c157ebf3%2Fbgbcq5j_processed.png&w=3840&q=75)
Transcribed Image Text: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:
for some unknown > 0. For this problem, we call Unif([0, 20], the first component.
First Initialization: EM for a Uniform Mixture
Assume that n = 8 and the observations are
5. Mixture of Uniforms
0₁
ƒ (x) = 1 (x = [0, 20]) + 11 (x = [0,30))
40
40
0₂
03
Assume that the EM algorithm is initialized at 00 = 3. What are the values of the first three iterates 01, 02, and 03 of the EM
algorithm?
||
X₁ = 1.01 X₂ = 1.02 X3 = 1.19 X₁ 1.19
X5 1.28 X6 = 2.39 X7 = 2.56 X = 2.58
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