6.872/HST950 Homework 2

Assigned:    3/2/2002
Due:            3/11/2002

1. In Dr. Issac Kohane’s lecture, he talked about an example of beads and Yankee winning a game. Assume the stadium holds 40,000 people, each people has a necklace of 20 beads, and each bead have 5 possible colors. By reviewing videos from the past 10 games in the stadium, you noticed situation A: sometime a person sat at the center seat in the 3rd row in the South section, wearing a necklace with a yellow bead in the middle line. In the past 10 games, situation A happened 5 times, and Yankee won. In the rest 5 games, situation A didn’t happened and Yankee lost.

a)      Discuss the probability that Yankee wins if situation A happens next time.

b)      You are curious about this association between the color of a specific bead and the result of the game, but you are not sure if it’s true. So you decide to observe a few more games. In the next 2 games, situation A happened, and Yankee won. Discuss the probability that Yankee wins if situation A happens after this observation.

c)      Discuss the problem of dimensionality and overfitting in bioinformatics, and suggest a few methods to deal with it.

2. In a certain population, three disorders – autosomal dominant retinoblastoma, autosomal recessive Friedreich’s ataxia (a neuromuscular disorder), and X-linked choroideremia (a cause of loss of vision in males at an early age) – each have a population incidence of ~1/25,000. Suppose that each one could be successfully treated, so that all selection against it was removed. What are the gene frequency (mutant genes) for each of these?

(Copied/modified from Genetics in Medicine by Thompson, McInnes, and Willard)

3. Dr. Marco Ramoni talked about five analysis methods: linkage analysis, allele sharing, association study, transmission disequilibrium test, and experimental cross. Please discuss the advantages and disadvantages of the five methods.

4. Sickle cell anemia is an autosomal recessive disorder caused by a defect in the HBB gene, which codes for hemoglobin. In the Unites States, it affects around 72,000 people, most of whose ancestors come from the Sub-Saharan region. The disease occurs in about 1 in every 500 African-American births. What is the proportion of African Americans are carriers of the disease?

5. In a genomic study, we have recruited 10 individuals and genotyped two consecutive loci. The alleles of the resulting 20 chromosomes are listed in the following table. Compute the degree of linkage disequilibrium between the two loci.