G********t
发帖数: 356 | 1 It's about some probability theory; I am really stuck on a small point and nee
d help urgently.
In some outside reading I
found Borel's "dactylography monkey" question, which states that with
probability equal to 1,a monkey hitting keys at random on a
typewritter will eventually type a copy of any given book. By
Kolmogorov's 0-1 law (that the probability of occurance of a tail
event is either 1 or 0) it's easy to see;but I came to the point of
proving the monkey's hitting keys is a tail event.
T | B****n
发帖数: 11290 | 2 This is the application of second borel cantelli lemma.
Suppose the number of letters in a book is n, the number of letters in a typew
ritter is m, then the probability of typing a book within n letters is
1/m^n. Let this event be A1. A2 is typing a book in next n letters. ....
sum(Ai)=infinity Ai are independent P(Ai io.)=infinity
【在 G********t 的大作中提到】
: It's about some probability theory; I am really stuck on a small point and nee
: d help urgently.
: In some outside reading I
: found Borel's "dactylography monkey" question, which states that with
: probability equal to 1,a monkey hitting keys at random on a
: typewritter will eventually type a copy of any given book. By
: Kolmogorov's 0-1 law (that the probability of occurance of a tail
: event is either 1 or 0) it's easy to see;but I came to the point of
: proving the monkey's hitting keys is a tail event.
: T
| G********t
发帖数: 356 | 3
thx! but what is P(Ai io.)?
【在 B****n 的大作中提到】
: This is the application of second borel cantelli lemma.
: Suppose the number of letters in a book is n, the number of letters in a typew
: ritter is m, then the probability of typing a book within n letters is
: 1/m^n. Let this event be A1. A2 is typing a book in next n letters. ....
: sum(Ai)=infinity Ai are independent P(Ai io.)=infinity
|
|
