[機統] 擲骰問題

[shancool (善)]

Let Xn be the sum of the first n outcomes of tossing a six-side die

repeated in an independent fashion.

Compute

           P(Xn is dibisible by 7) as n->∞


先謝謝各位了!!

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推 KitWoolsey  :1/7
→ KitWoolsey  :if Xn-1 is divisible by 7 --> Xn is not
→ KitWoolsey  :Xn-1 is not --> Xn has 1/6 chance div by 7
→ KitWoolsey  :so f(n) = {1-f(n-1) }/6
→ KitWoolsey  :so f(n) = 1/7 if it is to be stable