Изменения

<tex>\gamma_i(t) = p(Q_t=i\mid O,\;\lambda)=</tex> <tex dpi="160">\fracdfrac{\alpha_i(t)\beta_i(t)}{\displaystyle\sum^N_{j=1}\alpha_j(t)\beta_j(t)}</tex>

<tex>\xi_{ij}(t) = p(Q_t=i,\;Q_{t+1}=j\mid O,\;\lambda)=</tex> <tex dpi="160">\fracdfrac{\alpha_i(t)a_{ij}\beta_j(t+1)b_j(o_{t+1})}{\displaystyle\sum^N_{i=1}\displaystyle\sum^N_{j=1}\alpha_i(t)a_{ij}\beta_j(t+1)b_j(O_{t+1})}</tex>.

<tex>\bar{a}_{ij}=\fracdfrac{\displaystyle\sum^{T-1}_{t=1}\xi_{ij}(t)}{\displaystyle\sum^{T-1}_{t=1}\gamma_i(t)}</tex>,

<tex>\bar{b}_i(k)=\fracdfrac{\displaystyle\sum^T_{t=1}\delta_{O_t,\;o_k}\gamma_i(t)}{\displaystyle\sum^T_{t=1}\gamma_i(t)}</tex>.