I am doing my assignment and I am asked to derive transition probability of a HMM.
There are Three states. H, E and T.
They initially gave me the information as follow.
E is followed by an H 40% of the time and a T 60% of the time. H is followed by a E 30% of the time and a T 70% of the time. T is equally likely to be followed by a H or an E At the start of a sequence, any structure is equally likely.
Derive the transition probabilities of a state to itself by considering that if L is geometrically distributed with parameter p then E[L] = $\frac{1}{p}$. Also remember that $\Sigma_l a_{kl}=1$ for any state $k$.
What I did was
$H \to E = 0.3,\ H \to T = 0.7$ and therefore $H \to H = 0 $
$E \to H - 0.4,\ E \to T = 0.6$ and therefore $E \to E = 0$
$T \to H = 0.5,\ T \to T = 0.5$ and therefore $T \to T = 0$
But this seems to be wrong.
Is there a specific way to calculate the transition probability of this sort of problem or am I on the right track? If not, can someone please help me?