On 10/10/2008, at 6:16 AM, Harvey wrote:
Can someone recommend a method to answer the following type of
question:
Suppose I have a coin with a probability hhh of coming up heads
(and 1-hhh
of coming up tails)
I plan on flipping the coin nnn times (for example, nnn = 500)
What is the expected probability or frequency of a run of rrr
heads* during
the nnn=500 coin flips?
Moreover, I would probably (excuse the pun) want the answer for a
range of
rrr values, for example rrr = 0:50
Of course I am more interested in an analytical solution than a
monte carlo
simulation solution.
I think this is a relatively deep problem analytically, and there
appears to
be a substantial amount of literature. Googling on ``probability of
a sequence
of runs'' got a lot of hits, including a pointer to
http://mathworld.wolfram.com/Run.html
which gives some interesting discussion and provides a number of
references.
(Feller volume 1 seems to be a good place to start, as usual.)
cheers,
Rolf Turner
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