Así, paran∈\N,\ begin {align}\ P (N_t = n\ mid m_T = k) & =\ frac {\ P (N_t = n, m_T = k)} {\ P (m_T = k)} =\ frac {\ P (m_T = k, W_t = n - k)} {\ P (m_T = k)}\\ & =\ frac {\ P (m_T = k)\ P (W...Así, paran∈\N,\ begin {align}\ P (N_t = n\ mid m_T = k) & =\ frac {\ P (N_t = n, m_T = k)} {\ P (m_T = k)} =\ frac {\ P (m_T = k, W_t = n - k)} {\ P (m_T = k)}\\ & =\ frac {\ P (m_T = k)\ P (W_t = n - k)} {\ P (m_T = k)} =\ P (W_t = n - k)\ end {align} La forma de la función de densidad de probabilidad sigue desde Wtcomo la distribución de Poisson con parámetro(1−p)r.