Questions

1. (5 points) This is a followup on last week's first question, which was this:

   Assume that it is known that one person in a group of 100 committed a crime. You're in the group, so there's a prior probability of 1/100 that you are it. There is a pretty good forensic test. It makes errors (either way) only 0.1% of the time. You are given the test; the result is positive. Using this positive test, what's the probability now that you are the criminal? (Use Bayes.)

   With a lot of tests, the results are grey, and the person running them has a choice in how to interpret them: lean towards finding someone guilty (but falsely accusing an innocent person), or the other way toward finding someone innocent (but letting a guilty person go free).

   Assume that in this example, the administrator can choose the bias. However the sum of the two types of errors is constant at 0.2%. (Whether that relation is really true would depend on the test.)

   This question is to plot both the number of innocent people falsely found guilty and the number of guilty people wrongly let go, as a function of the false positive rate. Use any plot package. Both numbers of people will usually be fractional.

2. (5 pts) Do exercise 2.126, page 95.

3. (5 pts) Do exercise 2.127.

4. (5 pts) Do exercise 3.1 on page 130.

5. (5 pts) Do exercise 3.5.

6. (5 pts) Do exercise 3.13 on page 132.

7. (5 pts) Do exercise 3.15.

Total: 35 pts.