Give the formula for correlation of 1D continuous function.

The correlation of two continuous 1D functions can be calculated using the Pearson correlation coefficient, often denoted by \( \rho \). For two continuous functions \( f(x) \) and \( g(x) \), the Pearson correlation coefficient (\( \rho \)) is given by the following formula:

Here:

The formulas for covariance and standard deviation are as follows:

Note: The integral limits, in practice, are often finite and based on the specific range of interest for the functions. The integrals represent continuous summations over the entire range of the functions.