Patterns in sequences of random events
- 2003-11-07 (Fri.), 10:30 AM
- Recreation Hall, 2F, Institute of Statistical Science
- Professor Joe Gani
- Math. Sciences Institute, Australian National Univ., Canberra , Austra
Abstract
We begin with an early result recorded by Renyi (1984); in a sequence of n equiprobable independent Bernoulli trials, the number of sequences avoiding the repetition 00 is the Fibonacci number F(n+2). This can be generalized to the case where n independent trials may result in one of k>2 equiprobable mutually exclusive events. The analysis may be extended to the case where the k events are dependent, and form a Markov chain.
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