How to calculate the mean and standard deviation of parameters of a function that exists in both discrete and continuous version

There is a function that can exist in both discrete and continuous versions (the biological Lotka-Volterra equation), and I know how the parameters of one version can be calculated and converted by the parameters of the other. The thing is that I already have the estimated values of the mean and standard deviation of parameters of the discrete version, and I need to calculate the values of the continuous parameters. Since there are already formulas for calculating the continuous and discrete parameters from one another, I was wondering if I can calculate their mean and standard deviations through one another?


Both versions of the Lotka Volterra equation and the formulas for calculating their parameter through one another are as follows:

continuous version of the function is
and the discrete version is
and the formulas the parameters can be calculated through each other: