Final answer:
Based on the X-linked genotypes of their children, the mother's genotype is XaXa, and the father's genotype is XaYA.
Step-by-step explanation:
In order to determine the genotypes of the parents based on the genotypes of their children, we must understand how X-linked inheritance works. As two daughters have the genotype XaXA, we know that both must have inherited Xa from their mother and XA from their father.
Since one son has XaYa and the other has XaYA, it indicates the mother must also have an Xa allele to pass on, and the father must have both YA and Ya alleles to produce the different son genotypes. The father's Y chromosome alleles indicate pseudoautosomal inheritance, where some genes are shared between the X and Y chromosomes. Therefore, the mother's genotype must be XaXa, and the father's genotype must be XaYA.