Consider an array of real values as shown below

$x=[11\mathrm{.}55,11\mathrm{.}07,13\mathrm{.}31,10\mathrm{.}92,11\mathrm{.}89,13\mathrm{.}63,66\mathrm{.}46,73\mathrm{.}38,75\mathrm{.}38,73\mathrm{.}01,69\mathrm{.}44,68\mathrm{.}58].$

Assume that the random values are drawn from the two groups A and B with Gaussian distribution Each group has prior probability of $0\mathrm{.}5.$

Perform the Expectation$-$Maximization algorithm on the given data.

At the initial step, the A group has formed with Gaussian distribution with mean $2\mathrm{.}0$ and standard deviation $1\mathrm{.}5,$ and second group B has mean $7\mathrm{.}0$ and standard deviation $2\mathrm{.}0.$

Show all the steps for Expectation$-$Maximization on the give sample data for two iterations. Show the computed values such as likelihood for any sample $x_i,$ posterior probability, mean, and variance for each group.

$[6]$