A Connection between Correlation and Contingency

Let us consider a discontinuous bivariate distribution. That is, let us consider N × Q non-negative values p νq (ν = 1, 2, …, N; q = 1, 2, …, Q ), being the theoretical probabilities of the νth value of a variate X μ (μ = 1, 2, …, N ) concurring with the q th value of a second variate Y s ( s = 1, 2, …, Q ).