The paper demonstrates that random coefficient models can be estimated by maximum likelihood if they are specified as generalized least squares models. The paper uses maximum likelihood estimation on a random-coefficient, meat-demand system. Statistical tests show that price elasticities are random, but expenditure elasticities are not. The statistical tests allow one to count the number of factors that cause randomness without requiring one to know what they are. There appear to be only two factors that make the price elasticities random.