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WEEK 1 PROBLEMS. For your own good, it would be helpful to review the EASY problems at the end of Chapters 1, 2 and 3 (2nd edition). The answers are in the solutions guide.
1. Suppose the globe tossing data (Lecture 2, Chapter 2) had turned out to be 4 water and 11 land. Construct the posterior distribution.
2. Using the posterior distribution from 1, compute the posterior predictive distribution for the next 5 tosses of the same globe. I recommend you use the sampling method.
3. Use the posterior predictive distribution from 2 to calculate the probability of 3 or more water samples in the next 5 tosses.
4-OPTIONAL. This problem is an optional challenge for people who are taking the course for a second or third time. Suppose you observe W = 5 water points, but you forgot to write down how many times the globe was tossed, so you don’t know the number of land points L. Assume that p= 0.7 and compute the posterior distribution of the number of tosses N. Hint: Use the binomial distribution.
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