onlinetwodcorrelation:   Correlation coefficient of a discrete joint probability distribution P(x,y) Formulas P(x|y) = P(x,y)/P(y) P(y|x) = P(x,y)/P(x) s2x = Σ(x-x̄)2f(x) s2y = Σ(y-ȳ)2f(y) sx,y = Σ(x-x̄)(y-ȳ)f(x,y) rx,y = sx,y/(sxsy) Reference Ponce, V. M. 2014. Engineering Hydrology, Principles and Practices, Chapter 7, Section 1. Example INPUT DATA: Enter size of square array n (number n of x equal to number n of y):      Enter n Px(j) values (in any consistent units; separate each value with a comma): [Px (j, k) = Py (j, k) ]: Enter n2 Px,y(j,k) values (j varying first, k varying second; separate each value with a comma) [The sum of Px,y (j, k) values should equal 1]: ECHO OF INPUT: n =   OUTPUT: Variance sx = 0 Variance sy = 0 Covariance sx,y = 0 Correlation coefficient rx,y = 0   Your request was processed at  10:47:37 am on December 15th, 2025   [ 251215  10:47:37 ]. Thank you for running onlinetwodcorrelation.   Please call again.   [151030]