[機統] stationary distribution
題目可以看這裡
http://ppt.cc/K75N
A 5 state markov chain (states labeled {1,2,3,4,5}) is irreducible and has a
stationary distribution given by the vector
(1/3 1/27 7/27 1/27 1/3)
Then, assuming that the initial state is 2 and that it does not return to 2 in
the first 3 steps, find the expected number of times to return to 2.
(雖然這裡寫得很像要求"回到2的次數" 但是其實是要求"第一次回到2需要的steps")
Hint: use strong markov property to get rid of the first 3 steps, and then try
to compute the expectation in terms of the stationary distribution
以目前的條件可以直接算E2T2=27 不過這是當允許前三步回到2的時候
所以我想把E2T2寫成p21*E1T2+p22*0+p23*E3T2+p24*E4T2+p25*E5T2+1
先求出EXT2 for all states
但是我沒辦法從stationary distribution求出ExT2
而且就算我找出來 我也要知道第四步在哪裡才能求出期望值
我覺得自己的方向有錯
可是我想不出來要怎麼算
想請教一下版友
謝謝
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