correlation between binary strings

hi everyone I want to find the correlation between these two binary strings x and y

x=[1111111111111111111111111111111111111111111111111111111111111111];

y=[1000000001011001010110111110010101011010010000100010111101111110];

using the formula attached as figure. the value of E is 0.05 or 50%.

Thank you in advance

[Walter Roberson]

the value of E is 0.05 or 50%.

?? 0.05 would be 5% not 50% ?

Answer 1

[Maria Imdad]

0.05

[Walter Roberson]

If the values are represented by 0 and 1, then it seems to me using 0.5 would make more sense...

[Maria Imdad]

yes exactly

Answer 2

[Walter Roberson]

R = sum((x - E).*(y - E)) ./ (sqrt(sum((x-E).^2)) .* sqrt(sum((y-E).^2)));

[Maria Imdad]

will this formula compare and compute correlation between each corresponding bit? because i want it to iterrate for all 64 bits

[Walter Roberson]

It handles all of x and all of y, assuming that they are the same size. It uses vector operations so it does not need to loop. The sigma operation in the equation is sum() here.