In a Gaussian Mixture Model (GMM) with two components, the parameters are as follows: - Component 1: Mean (\mu_1) = 2, Variance (\sigma_1^2) = 1, Mixture Proportion (\pi_1) = 0.6 - Component 2: Mean (\mu_2) = 5, Variance (\sigma_2^2) = 2, Mixture Proportion (\pi_2) = 0.4 Given a data point x = 3, calculate the responsibilities (posterior probabilities) for each component. Hint: \mathcal{N}(x \mid \mu, \sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)

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Algorithmic Thinking in Bioinformatics · Quiz 2 · 3 Aug 2025 · May 2025 term

Question 3: In a Gaussian Mixture Model (GMM) with two components, th…

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In a Gaussian Mixture Model (GMM) with two components, the parameters are as follows:

Component 1: Mean $(\mu_1) = 2$ , Variance $(\sigma_1^2) = 1$ , Mixture Proportion $(\pi_1) = 0.6$
Component 2: Mean $(\mu_2) = 5$ , Variance $(\sigma_2^2) = 2$ , Mixture Proportion $(\pi_2) = 0.4$

Given a data point $x = 3$ , calculate the responsibilities (posterior probabilities) for each component. Hint:

$\mathcal{N}(x \mid \mu, \sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)$

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Question 3 of 18 in the IIT Madras BS Algorithmic Thinking in Bioinformatics (Algorithmic Thinking in Bioinformatics) Quiz 2 paper sat on 3 Aug 2025, in the May 2025 term (IIT M IMPROVEMENT AN EXAM QIA2 03 Aug 2025). It carries 3 marks.

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