[機統] transient/recurrent
可以看這裡
http://ppt.cc/T4vl
題目是
Consider independent tosses of a fair die. Let Zn{1,2,3,4,5,6} be the result of
the n-th toss and let Xn+1=max{Xn,Zn} for n>=1, X1=Z1
前兩題我會算
c) for each transient x and recurrent y, find ExTy, where Ty is the time of the
first return to y.
因為只有6是recurrent 而E5T6是geometric 所以這個是1/p=6
但是當我算E4T6時
我把她歸類為2種情況
444...446或4...45
∞ ∞
E4T6=Σ(k+6)*(1/6)*(4/6)^(k-1)+Σ(k)*(1/6)*(4/6)^(k-1)=6
k=1 k=1
可是我以為從4開始的話E會比從5開始還大
是我哪裡算錯了嗎?
謝謝
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04/17 13:19, , 1F
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