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October 5th, 2009, 03:01 AM   #1
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Prior probability of selecting an alphabet character puzzler

Hi,
I have a mathematical problem that I'm working on and I was hoping someone might be able to help.
I'm trying to find the probability of selecting any letter from the alphabet, given a 'prior probability' (I think that's what it is anyway).
So here are my figures.
13062 characters were hit on a keyboard and here is what was found:
a has 938 occurrences
b has 9 occurrences
c has 1 occurrences
d has 2 occurrences
f has 7 occurrences
g has 582 occurrences
h has 56 occurrences
j has 105 occurrences
k has 3 occurrences
l has 43 occurrences
m has 24 occurrences
n has 16 occurrences
p has 3 occurrences
q has 1304 occurrences
s has 9925 occurrences
v has 44 occurrences
All the other characters were not hit.
So, we can see there is a preference for some characters (e.g. s, a, g, etc) over others (e.g. e, i, o, r, etc - which were never selected).
What I want to do is simulate the selection of more characters (a-z), and have that selection follow the pattern of the above characters, but also allow for the chance of a character that isn't hit in the list above to be included.
From doing some reading, I suspect that I will have to apply some sort of Bayesian approach, but don't know if this is the case and wouldn't know how to do this anyway.
A working example of how to work out the probability of a listed and unlisted character would also be REALLY appreciate!

Any takers?
Many thanks.
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