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Machine Learning Techniques · Quiz 1 · 26 Oct 2025 · September 2025 term

Question 12: Suppose at the t-th iteration of the EM algorithm, the p…

Question 12

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Suppose at the tt-th iteration of the EM algorithm, the parameters are:

π1=0.3,π2=0.7,μ1=2,μ2=3,σ12=1,σ22=1.\pi_1 = 0.3, \quad \pi_2 = 0.7, \quad \mu_1 = 2, \quad \mu_2 = 3, \quad \sigma_1^2 = 1, \quad \sigma_2^2 = 1.

The densities of the data points given each mixture component are provided below:

xix_if(xi∣zi=1)f(x_i \mid z_i = 1)f(xi∣zi=2)f(x_i \mid z_i = 2)
10.2420.054
100.3990.242
200.2420.399

What is the value of λ11\lambda_1^1? Enter your answer correct to two decimal places.

Show answer

Correct answer: 0.66 (accepted within ±0.02)

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Question 12 of 14 in the IIT Madras BS Machine Learning Techniques (MLT) Quiz 1 paper sat on 26 Oct 2025, in the September 2025 term (IIT M DIPLOMA AN EXAM QDD2 26 Oct 2025). It carries 3 marks.

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