31 Matching Annotations
  1. Mar 2024
  2. Jan 2024
    1. Pero por la propiedad Markov, esto se reduce a\ begin {align*}\ P (X_0 = x_0, X_1 = x_1,\ ldots, x_n = x_n) & =\ P (X_0 = x_0)\ P (X_1 = x_1\ mid X_0 = x_0 = _0)\ P (X_2 = x_2\ mediados X_1 = x_1)\ cdots\ P (X_n = x_n\ mediados X_ {n-1} = x_ {n-1})\\ & = f_0 (x_0) P (x_0, x_1) P (x_1, x_2)\ cdots P (x_ {n-1}, x_n)\ final {alinear*}

      Pero por la propiedad Markov, esto se reduce a $$ \begin{align} P (X_0 = x_0, X_1 = x_1,\ldots, x_n = x_n) & =P (X_0 = x_0) P (X_1 = x_1\mid X_0 = x_0 = 0) P (X_2 = x_2\mid X_1 = x_1)\cdots P (X_n = x_n\mid X {n-1} = x_ {n-1})\ & = f_0 (x_0) P (x_0, x_1) P (x_1, x_2)\ cdots P (x_ {n-1}, x_n) \end{align} $$