Suppose a birth defect has a recessive form of inheritance. In a study population, the recessive gene (a) initially has a prevalence of 25%. A subject has the birth defect if both maternal and paternal genes are of type a. A further study finds that after 10 generations (≈200 years) a lot of inbreeding has taken place in the population. Two subpopulations (populations A and B), consisting of 30% and 70% of the general population, respectively, have formed. Within population A, prevalence of the recessive gene is 40%, whereas in population B it is 10%. Suppose that a baby is born with a birth defect, but the baby’s ancestry is unknown. What is the posterior probability that the baby will have both parents from population A, both parents from population B, or mixed ancestry, respectively? (Hint: Use Bayes’ rule.)
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Suppose a birth defect has a recessive form of inheritance.
In a study population, the recessive gene (a) initially has a
prevalence of 25%. A subject has the birth defect if both
maternal and paternal genes are of type a.
A further study finds that after 10 generations (≈200 years)
a lot of inbreeding has taken place in the population. Two
subpopulations (populations A and B), consisting of 30%
and 70% of the general population, respectively, have
formed. Within population A, prevalence of the recessive
gene is 40%, whereas in population B it is 10%.
Suppose that a baby is born with a birth defect,
but the baby’s ancestry is unknown. What is the posterior
probability that the baby will have both parents from population A, both parents from population B, or mixed ancestry,
respectively? (Hint: Use Bayes’ rule.)
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