Consider the Girl$-$and$-$Tiger example discussed in the class. Suppose that at time t $=0,$ the probabilitiesfor the tiger to be behind the left door and the right door are $(0\mathrm{.}5,0\mathrm{.}5).$ Answer the following questionsusing the state$-$transition and the observation models in the lecture slides.$($a$)(4$ Points$)$ If the girl always chooses to listen and gets a sequence of observations,$($TL$,$TR$,$TR$,...),$whatis the probability distribution of the tigers location at time t $=1,2,3,$ respectively?$($b$)(4$ Points$)$ If we additionally allow the tiger to jump to the opposite room with probability $0\mathrm{.}1$ ateach time step, what is the probability distribution over the tigers position at time t $=1,2,3,$after receiving the same sequence of observations?