$\backslash [$ E$=\backslash$left$[\backslash$begin$\{$array$\}\{$cccccc$\}1/6$ & $1/6$ & $1/6$ & $1/6$ & $1/6$ & $1/6\backslash \backslash 1/10$ & $1/10$ & $1/10$ & $1/10$ & $1/10$ & $1/2\backslash$end$\{$array$\}\backslash$right$]\backslash ]3$ And the state transition matrix is $\backslash [$ P$($F $\backslash$mid F$)=0\mathrm{.}95,\backslash$quad P$($L $\backslash$mid F$)=0\mathrm{.}05,\backslash$quad P$($L $\backslash$mid L$)=0\mathrm{.}9,\backslash$quad P$($H $\backslash$mid L$)=0\mathrm{.}1.\backslash ]$ Assume the observed sequence is $666141.$ Assume the initial distribution to be

$[1/2,1/2]$

$.$ Answer the following questions. You can implement the Viterbi algorithm on computer for your computation $($then you have to also submit the code$),$ or calculating by hands $($make sure to show your calculation$).($a$)(10$ points$)$ Calculate

P$($S

$3$

$$

$=$L$"266641")=$

$?($b$)(10$ points$)$ What is the most likely sequence of states given all the observations: $"236641"?$