Practice the following exercises to reinforce the concepts learned in this chapter:
- Recall the drug testing at Daisy Girl, Inc. earlier in the chapter. We used .1% as our prior probability that the employee was using the drug. Why should this prior have been even lower? Using a subjective Bayesian interpretation of probability, estimate what the prior should have been given that the employee was able to hold down a job and no one saw her/him act like an alligator.
- Hark back to the example of the coin from Larry the Untrustworthy Knave. We would expect the proportion of heads in a fair coin that is flipped many times to be around 50%. In Larry's coin, the proportion was 2/3, which is unlikely to occur. The probability of 20 heads in 30 flips was 2.1%. However, find the probability of getting 40 heads in 60 flips. Even though the proportions are the same, why is...
