On Tue, 29 Apr 2008, Anthony28 wrote:
I need to use R to model a large number of experiments (say, 1000). Each
experiment involves the random selection of 5 numbers (without replacement)
from a pool of numbers ranging between 1 and 30.
What I need to know is what *proportion* of those experiments contains two
or more numbers that are consecutive. So, for instance, an experiment that
yielded the numbers 2, 28, 31, 4, 27 would be considered a "consecutive =
true" experiment since 28 and 27 are two consecutive numbers, even though
they are not side-by-side.
I am quite new to R, so really am puzzled as to how to go about this. I've
tried sorting each experiment, and then subtracting adjacent pairs of
numbers to see if the difference is plus or minus 1. I'm also unsure about
whether to use an array to store all the data first.
Any assistance would be much appreciated.
Are the numbers 1:30 equiprobable??
If so, you can find the probability by direct enumeration.
mat <- combn(30,5) # each column happens to be in order
tab <- table( mat[2:5,]-mat[1:4,]==1, col(mat[1:4,]) )
table(tab[2,])
0 1 2 3 4
65780 59800 15600 1300 26
prop.table( table(tab[2,] != 0 ) )
FALSE TRUE
0.4615946 0.5384054
If the numbers are not equiprobable, you will need to weight the values of
tab[2,] according to the probability of each column of mat.
HTH,
Chuck
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Charles C. Berry (858) 534-2098
Dept of Family/Preventive Medicine
E mailto:[EMAIL PROTECTED] UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901
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