Calculation of the correlation coefficient of random variables using additional information about the form of their relationship

The problem of calculating the correlation coefficient of two random variables is considered under the assumption that the mathematical expectation of their product is unknown, but the first two moments of the distribution of each of them are known. The solution is proposed for the case when the set of possible values of one quantity depends in a certain way on a fixed value of another quantity. It is shown that with the use of additional information about the form of the relationship of the studied random variables, it is possible to significantly simplify the calculation of the correlation coefficient.