The estimation of allele probabilities is essential for the
closer quantitative identification of inheritance. It requires
the probabilistic formulation of the applied model of inheritance. The hereditary disease phenylketonuria (PKU) is a
useful example. PKU follows a recessive form of inheritance.

Suppose there are two alleles at a gene locus denoted by
a and A where the possible genotypes are (aa), (aA), and
(AA). An individual will only be affected if the genotype aa
appears (i.e., a recessive form of inheritance).

As an experiment, 10,000 people are completely genotyped, of whom 10 have the (aa) genotype, 630 have the
(aA) genotype [i.e., either (aA) or (Aa)], and 9360 have the
(AA) genotype.

(1)  If the two alleles of an individual are independent
random variables, then provide a point estimate and a 95%
CI for the a allele frequency p.

The estimation of allele probabilities is essential for the
closer quantitative identification of inheritance. It requires
the probabilistic formulation of the applied model of inheritance. The hereditary disease phenylketonuria (PKU) is a
useful example. PKU follows a recessive form of inheritance.

Suppose there are two alleles at a gene locus denoted by
a and A where the possible genotypes are (aa), (aA), and
(AA). An individual will only be affected if the genotype aa
appears (i.e., a recessive form of inheritance).

Suppose that on a population level it is impossible to genotype large numbers of individuals. However, it is known that
among 10,000 people surveyed in the population, 11 have
the PKU clinical phenotype.

As an experiment, 10,000 people are completely genotyped, of whom 10 have the (aa) genotype, 630 have the
(aA) genotype [i.e., either (aA) or (Aa)], and 9360 have the
(AA) genotype.

(1) If the two alleles of an individual are independent
random variables, then provide a point estimate and a 95%
CI for the a allele frequency p.