= Solution
The <pedigree founder> factor $P(G_i)$ depends on population <allele> and <haplotype> frequencies, ancestry, mating assumptions and any population <linkage disequilibrium>. At one autosomal <genetic locus>, <Hardy-Weinberg equilibrium> with <allele> frequencies $p,q$ gives <genotype> <probabilities> $p^2,2pq,q^2$. For a specified ordered pair of independent <pedigree founder> <haplotypes> $h_1,h_2$, the <probability> is $p_{h_1}p_{h_2}$; an unordered distinct pair has twice that <probability>. <Pedigree founders> assumed to be related require a joint prior rather than a product of unrelated-founder factors.
The nonfounder factor depends on the parental <genotypes> and phases, <Mendelian segregation>, and the <recombination fractions> between <genetic loci>. In a two-locus <heterozygote> of known phase, the two parental <haplotypes> have transmission <probabilities> $(1-\theta)/2$ each, and the two recombinant <haplotypes> $\theta/2$ each. Multiply the maternal and paternal gamete <probabilities> and sum any gamete combinations producing the child's <genotype>. Sex-specific <genetic recombination>, mutation or segregation distortion can be incorporated by changing these gamete <probabilities>. At one ordinary autosomal <genetic locus>, each parental copy is transmitted with <probability> $1/2$.
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