Relationships Among the Parameters of Milk Production, Constituent Production, and Constituent Percentage

A method of finding the parameters pertaining to one of the variables of milk production, constituent production, and constituent percentage when the parameters pertaining to the two other variables are known is presented. The method is based on the expectation of products of random variables. This method and the delt~ approximation method are compared to sampling estimates from simulated data. Knowledge of the parameters of any two of milk production, constituent production, and constituent percentage can be used to find the parameters pertaining to the third. Eisen (1) presented formulae giving these relationships, the formulae being based on the delta approximation presented in Kendall and Stuar t (3). Alternative formulae are presented here, these being based on known expectations of the products of two, three, or four normally distributed variables. The case of milk production, milk fa t production, and milk fa t percentage (test) is used as an illustration. The mean of milk fat production can be found