Exercises
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 the probability of observing 40 heads in 60 flips so significantly less probable? Understanding the answer to this question...
