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Journal of Dairy Science Vol. 53 No. 9 1248-1258
© 1970 by American Dairy Science Association ®
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Some Probabilities Deriving from Dairy Sire Evaluation Models

F. R. Allaire

Department of Dairy Science, The Ohio State University, Columbus 43210

ABSTRACT

Probabilities were illustrated for two models in dairy sire evaluation. The production information on the daughters of each sire was assumed to be summarized into a proof by selection index principles. The proof (P) and the true daughter average (U) (i.e., the average production for an infinitely large number of daughters on each sire) was assumed to have a bivariate normal distribution. The probabilities illustrated for a population of sires were the probability a) that transmitting ability exceeds the breed average, b) of correctly ranking a pair of sires, c) of correctly ranking two groups of sires, and d) that a random cow will have a record exceeding her expected herdmate average. Theoretical probabilities can be expected to differ from proportions observed in practice in relation to the applicability of the model providing the probabilities.







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