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Homework Assignment 2

1. Among 521 duodenal ulcer patients gathered by Clarke et al. (1959), the

following ABO bloodtypes were observed: A = 186, B = 38, AB = 13, and O =

284. Formulate a likelihood for estimating the three allele frequencies

underlying the ABO blood group. Use the EM-algorithm to find the

likelihood estimates. Give explicit description of the the E and M steps.

In the above formulation of the EM-algorithm you assumed HWE. Are the data

consistent with this assumption? To answer the question conduct a

significace test and make a decision based on a p-value.

2. In section 2.4.2, Shaw proposes an EM-algorithm to estimate the

(phenotypic) segregation ratio for a rare recessive trait based on

heterozygous matings (Dd X Dd). Formulate the likelihood based on the

observed data, and develop (in detail) an EM-algorithm that follows

equation 2.22. Confirm the EM results in Example 2.8.

Due: Feb 24.