Consider the following given data.

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$\backslash$table$[[$SI num,Data$],[1,16\mathrm{.}9],[2,3\mathrm{.}7],[3,18\mathrm{.}9],[4,5\mathrm{.}6],[5,14\mathrm{.}1],[6,6\mathrm{.}1]]$

It is required to obtain two groups from the above given data into clusters A and B$.$ Both the groups are represented with the Gaussian distribution. For cluster, A is initialized with a mean of $5\mathrm{.}0$ and standard deviation of $1\mathrm{.}0$ while cluster $B$ is initialized with a mean of $10\mathrm{.}0$ and standard deviation of $1\mathrm{.}5.$ Perform the cluster based on the Expectation$-$Maximization technique assuming the prior probabilities of each cluster A and $B$ is $0\mathrm{.}5.$

Show the two iterations of the Expectation$-$Maximization technique and each iteration compute the likelihood, posterior probabilities, mean, and variance for each cluster.

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