Consider the relative frequencies of letters in general Engl

Consider the relative frequencies of letters in general English plain text (see handout posted on course webpage). Do the reported frequencies sum to 1? Calculate the entropy. You can use Matlab to do the calculation. Relative Frequencies of Letters in General English Plain text From Cryptographical Mathematics, by Robert Edward Lewand

Solution

pro = [0.08167 0.01492 0.02782 0.04253 0.12702 0.02228 0.02015 0.06094 0.06996 0.00153 0.00772 0.04025 0.02406 0.06749 0.07507 0.01929 0.00095 0.05987 0.06327 0.09056 0.02758 0.00978 0.02360 0.00150 0.01974 0.00074];

a = size(pro);
temp = 0;
sum=0;
for inc = 0:a
i = -pro(inc)*log(2,pro(inc));
temp = temp + i;
sum = sum + pro(inc);
end
disp(\'entropy\',temp);
if(sum==1.0000)
disp(\'probabilityReportedto1\');
else
disp(\'probabilityNotReportedto1\');
end

Answer:

entropy 4.1764911000

probablityNotReportedto1