作者nourri (nourri)
看板Statistics
标题Fw: [机统] stationary distribution
时间Wed Apr 24 04:02:58 2013
※ [本文转录自 Math 看板 #1HTX-wwe ]
作者: nourri (nourri) 看板: Math
标题: [机统] stationary distribution
时间: Tue Apr 23 13:44:24 2013
题目可以看这里
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.
(虽然这里写得很像要求"回到2的次数" 但是其实是要求"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
以目前的条件可以直接算E2T2=27 不过这是当允许前三步回到2的时候
所以我想把E2T2写成p21*E1T2+p22*0+p23*E3T2+p24*E4T2+p25*E5T2+1
先求出EXT2 for all states
但是我没办法从stationary distribution求出ExT2
而且就算我找出来 我也要知道第四步在哪里才能求出期望值
我觉得自己的方向有错
可是我想不出来要怎麽算
想请教一下版友
谢谢
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※ 转录者: nourri (76.171.77.30), 时间: 04/24/2013 04:02:58