$($a$)[5$ points$]$ Assume we run EM starting from an initialization of $1=2$ and $2=2.$ Please decide the value of $1$ and $2$ at the next iteration of EM algorithm. $($You may find it handy to know that $1/(1+$ exp$(4))0\mathrm{.}98).($b$)[5$ points$]$ Do you think EM $($when initialized with $1=2$ and $2=2)$ will eventually converge to $1=1$ and $2=1($i$.$e$.,$ coinciding with the two data points$).$ Please justify your answer using either your theoretical understanding or the result of an empirical simulation. $($c$)[5$ points$]$ Please decide the fixed point of EM when we initialize it from $1=2=2.($d$)[5$ points$]$ Please decide the fixed point of K$-$means when we initialize it from $1=2$ and $2=2.$