A possible Hidden Markov Model (HMM)

Figure shows a simple hidden Markov model for identifying a gene. Assuming probability p for staying in an exon state, the exon state length has a geometric distribution:

$$\begin{eqnarray*}P(\mbox{exon of length }k) = p^k\times(1-p) \end{eqnarray*}$$

Since an HMM is a memory-less process, the only length distribution that can be modeled is geometric.

  

Figure: Simple HMM for eukaryotic genes [].