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In mathematical genetics, a genetic algebra is a (possibly non-associative) algebra used to model inheritance in genetics. Some variations of these algebras are called train algebras , special train algebras , gametic algebras , Bernstein algebras , copular algebras , zygotic algebras , and baric algebras (also called weighted algebra ).
For example, Mendel found that if you cross heterozygous organisms your odds of getting the dominant trait is 3:1. Real geneticist study and calculate probabilities by using theoretical probabilities, empirical probabilities, the product rule, the sum rule, and more. [47]
The product-to-sum identities [28] or prosthaphaeresis formulae can be proven by expanding their right-hand sides using the angle addition theorems. Historically, the first four of these were known as Werner's formulas , after Johannes Werner who used them for astronomical calculations. [ 29 ]
The FOIL rule converts a product of two binomials into a sum of four (or fewer, if like terms are then combined) monomials. [6] The reverse process is called factoring or factorization . In particular, if the proof above is read in reverse it illustrates the technique called factoring by grouping .
In genetics, Bayes' rule can be used to estimate the probability that someone has a specific genotype. Many people seek to assess their chances of being affected by a genetic disease or their likelihood of being a carrier for a recessive gene of interest.
The sum of the entries is p 2 + 2pq + q 2 = 1, as the genotype frequencies must sum to one. Note again that as p + q = 1, the binomial expansion of (p + q) 2 = p 2 + 2pq + q 2 = 1 gives the same relationships.
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