Learn the E and M steps with two groups and hidden labels.

Use allele counting and an HWE likelihood, then add genotyping error with latent genotypes and EM.

Change transition and emission assumptions, then watch how the posterior probabilities respond.

Use a copying model to connect haplotypes, linkage disequilibrium, recombination, hidden states, and genotype imputation.

Use a small hidden Markov model to see why a run of matching markers supports a shared ancestral segment.

Follow a disease-associated marker through informative meioses and compare linked and unlinked models.

Compare IBD sharing among affected siblings with the Mendelian expectation.

Average genotype differences across independent SNPs and recover the expected kinship of unrelated pairs and siblings.

Run PCA and the ancestry model on toy genotypes, then apply the functions to the separate homework data.

Follow neutral allele frequencies in small and large populations; compare diversity loss with the Wright–Fisher prediction.

Follow two populations as they exchange migrants and see why pooling their genotypes can create a heterozygote deficit.