February 24, 2000

Notes for February 24, 2000

 Segment Time Collect Journals. Collect homework Discuss Rodney King questions: Investigate whether "chance" is a reasonable explanation for all pursuing officers being white? Suppose you are a member of the California Supreme Court and that before you is the matter of what level of likelihood may be taken as "evidence of racial bias in police dispatching procedures." What level would you set for that and future cases? What does the idea of probability, or "behavior in the long run," have to do with these questions? Review: Process (experiment) Outcome Sample space Exercise 2.10 (p. 16). What is the process? What is an outcome? What is the sample space? Discuss homework (HIV): Translate HW question: What fraction of the those people who test positive actually have HIV? TEST YES TEST NO HIV HIV YES 98% of 0.5% 2% of 0.5% HIV NO 2% of 99.5% 98% of 99.5% Take a visual approach: US Census Bureau table. Ask, for example, these questions: What fraction of the US population is White? Black? Native? What fraction of the US population is Hispanic? Black Hispanic? Native Hispanic? What fraction of Native Americans are Hispanic? What fraction of all Hispanics are white? I say, "Pick a US citizen at random. What is the probability this person is Native American?" What does this mean? (When you pick a person at random many times, what fraction of those times …) Why can we say this? (We expect the composition of large simple random samples to reflect the population's composition.) KEY!!!! (Large samples are made by picking individuals one at a time!) I say, "Pick a Hispanic person at random. What is the probability this person is Asian? What does this mean? What is your answer? Homework (Tomorrow, Friday, show the table also and then the tree diagram as a shortcut to the table and diagram. But STRESS that the tree diagram is not a SUBSTITUTE for the others. Rather, it is a way to reason the same way without having to write so much down. My intention for these questions is to have students start thinking in this way: That is, students now tend to think of probability of events over the long run, but each event has its own "long run." When they think that way, then they cannot see a link between long-term behavior and sample space. Rather, they understand the link between long-term behavior and sample space when they understand that the long-term behavior of a process in relation to one outcome entails relationships to the other possible outcomes, too. So, we need to emphasize that we need only think of one long-run sequence of trials in order to imagine the probability of any of the processes possible outcomes. When every outcome has its on long-term repetition of the process, then there is no way to imagine each in relation to the other. The long-runs are, in a sense, independent of each other. They need to be imagined in relation to each other, and imagining them all being contained within a single long run of the process does that.