Gaussian Mixture Model: An Example Update $-$ M$-$Step

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Compute the updated parameters corresponding to cluster $1($provide at least five decimal digits$)$:

hat$(p{)}_1=$

$$

hat$({)}_1=$

$$

hat$({)}_1^2=$

$$

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Gaussian Mixture Model and the EM Algorithm

$1$ point possible $($graded$)$

Which of the following statements are true? Assume that we have a Gaussian mixture model with known $($or estimated$)$ parameters $($means and variances of the Gaussians and the mixture weights$).$

A Gaussian mixture model can provide information about how likely it is that a given point belongs to each cluster.

The EM algorithm converges to the same estimate of the parameters irrespective of the initialized values.

An iteration of the EM algorithm is computationally more expensive $($in terms of order complexity$)$ when compared to an iteration of the K $-$means algorithm for the same number of clusters.