Mixture responsibilities and EM

Problem

At a data point $x$ , two Gaussian-mixture components have prior weights $0.4$ and $0.6$ and component densities $p(x\mid z=1)=0.3$ and $p(x\mid z=2)=0.1$ . Compute posterior responsibilities and state the E- and M-step roles.

Reveal answer or reference solution

The unnormalized weights are $0.12$ and $0.06$ , so the responsibilities are $\frac{2}{3}$ and $\frac{1}{3}$ . The E-step computes responsibilities; the M-step updates parameters using those expected assignments.

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Unsupervised Learning Practice