Mathematical models of geometric sizes of coffee beans as dependent random variables

Dimensions of 100 randomly selected coffee beans of the Arabica and Robusta variety were determined by measuring their length (l), width (b) and thickness (h). The results of the measurements were processed by the methods of mathematical statistics. Parameters of distributions of separate sizes as random variables are determined. By the value of the coefficient of variation, the density function of normal distribution (Gaussian distribution) is taken as a model of separate sizes of beans. Models of two-dimensional distributions of beans sizes as independent random variables are presented. The coefficients of correlation between the geometric sizes of beans are calculated. The obtained values of the correlation coefficients indicate that the geometric sizes of beans should be considered as dependent random variables. The mathematical models of geometric sizes of beans as dependent random variables as density functions of their normal distribution are proposed. By values of the sums of squared deviations as a fitting criterion it has been established that the mathematical models of geometric sizes of beans as dependent random variables in the form of density functions of their normal distribution provide better data approximation than the mathematical models of geometric sizes of beans as independent random variables.