Here is a list of some Fermi problems for you to think about.

In class I mentioned that if you have a good idea how to do those Fermi problems, you should do fine on any question about them.

We looked at all but the last bullet point. Every bullet point has a homework or class discussion behind it (you can look earlier in the blog to find the discussions).

The questions on probability are summed up in the Independence and More Independence homework problems.

The Monty Hall problems were done in class, and the King and Brothers problem was homework. Imagine how I might alter these questions by, for example, changing the number of doors in Monty Hall, or the number of children in King and Brothers.

The cancer problem is exactly like the cancer problem we did in class as far as getting the posterior probabilities (1-2). Number 3, predicting the probability of someone having a positive test getting cancer is like the last part of the cookies problem in Problem Set #3. That is, once you have the posterior probability that someone has the gene after the test is done, you then use the 0.2 and 0.0002 probabilities to predict the probability of getting cancer. We discussed this part in class…it is the “posterior predictive” aspect of the cookie problem.

The galaxy problem is just the Shakespeare vs. Marlow problem in different guise.

The plagiarism problem points out that if you have a 5 as the last calculated digit, you should round up or down randomly, or else you would build a bias into your table. That would not be good. But you can use this to prove plagiarism, because in the example there are about 100 numbers where you round randomly up or down, and the probability that someone would independently get the same rounding pattern by accident is 2^{-100}, or about 10^{-30}. This would be very convincing evidence in a copyright suit.

The first urn problem is basically the fish “catch and release” problem, done several times.

The second urn problem is basically the tank counting problem.

The beetle and ant problem is like the problem we did in estimating the cure rate of a disease.

I asked you to think about the decision problem over the next few days. We will discuss it on Wednesday.

General comments: I want to know on the quiz if you know how to solve these problems. The premium will be placed on your clear explanation of what needs to be done, e.g., explain the prior you used, explain how the likelihood is calculated, and what you do next. You do not necessarily have to compute numbers in most cases, especially if the calculation involves many lines of a spreadsheet. Just convincing me that you know exactly what needs to be done should be sufficient. Of course, if I ask you for a number, you do need to calculate it.

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