## Genetics for Probability

To provide a scientific context for our probability problems, we will use examples from genetics. Genetics is almost unique among the sciences, in that its fundamental laws were stated as probability laws. Thus the probabilities we compute have a reality as long-run frequencies, and are not just subjective. For example, the probability a parent of blood-type O has a child of blood-type O is the proportion of times this event occurs among all children of all parents of blood type O. However, the probability President Clinton will resign cannot be given this interpretation, and is known as a subjective probability.

Other advantages of genetics are that the basic laws can be very simply and briefly stated, but that it also provides examples of the full range of probability ideas we encounter in MATH/STAT 394-5-6. A disadvantage is that there is some basic terminology and facts to learn. These will be kept to a minimum.

Anna Schneider, a UW senior, wrote some notes on these basic laws and terminology, as part of an Undergraduate Summer Research Project, in Summer 1998. We owe her a big thank you -- without her work, this would be a lot harder.

The examples (for example 2.3) are intended just to make sure you understand. The problems (for example 2.4) should be straightforward -- again these are just to make sure you are following ok. If you have difficuly with any of these problems/examples PLEASE LET ME KNOW. Note that Anna has not taken probability. Where she writes "what proportion", that just means "what is the probability". Where she writes "how many...", I have edited it to "on average, how many ..." ... that is just the number times the probability for each -- remember a probability is just a long-run frequency.

1. Introduction to Genetics

• 1.1 DNA and Chromosomes
• 1.2 Alleles of a gene
• 1.3 Genotypes and phenotypes

2. Mendelian segregation

• 2.1 Mendel's first law
• 2.2 Examples 1
• 2.3 Problems 1
• 2.4 Mendel's experiments

3. Population allele frequencies

• 3.1 Population allele frequencies
• 3.2 Examples 2
• 3.3 Problems 2

• 4.2 Examples 3
• 4.3 Problems 3

5. Joint inheritance of traits

• 5.1 Two indep inherited traits
• 5.3 Problems 4

6. Recombination as a Poisson process

• 6.1 Haldane's recombination model
• 6.2 Problems 5
• 6.3 Problems 6

7. Binomial and multinomial counts

• 7.1 Offspring types, probabilities, and counts
• 7.2 Problems 7

8. Normal approximations and normally distributed genetic traits

• 8.1 Mendel's experiments revisited: are his results too good?
• 8.2 Problems 8: Normal approximations to binomial counts
• 8.3 Standardized height, and correlations among relatives
• 8.4 Problems 9: some bits and pieces on continuous dsns

9. The process of meiosis

• 9.1 Meiosis