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I took recently my first class, but I don't quite understand how can I prove the equality.

Show that for every $i_0$, $i_1$, . . . , $i_{n−1}$, $i_n$, $j_1$, $j_2$ ∈ E and n ∈ $N_0$ the following below is valid.

P($X_{n+2}$ = $j_2$, $X_{n+1}$ = $j_1$ | $X_n = i$, $X_{n−1}$ = $i_{n−1}$, . . . , $X_0$ = $i_0$) = P($X_{n+2}$ = $j_2$, $X_{n+1}$ = $j_1$|$X_n = i$)

Thank you.

Lella
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Oleg
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  • It says that knowing what happened yesterday, the day before yesterday, the day before that,..., etc. does not tell you anything about tomorrow. Only today's information could have an effect over tomorrow's state. – YoTengoUnLCD Nov 06 '16 at 21:37
  • @YoTengoUnLCD I understood that part :) but how can I prove that the left side really equals the right side ? I don't have any idea – Oleg Nov 06 '16 at 21:47

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