Problems (p53-58): 3, 7, 11, 12, 18, 21, 32; (p104-115): 6, 12, 21, 39, 50.
Theoretical exercises (p59-61): 6,18,19; (p115-119): 2, 6, 8.
Bonus question:
Recall the "test" problem discussed in class. A certain disease affects one in every 105 individuals. A test for a disease is available and is such that if a person is infected then he/she will always test positive and a healthy person tests positive with probablity .02 (in other words, the probability of false positive is .02). Suppose that a certain individual has been tested k times and the test came up positive all k times. Assuming that the false positives happen completely at random (that is, the tests can be assumed independent even if done on the same individual), how large should k be to ensure that the probability that the person has the disease having tested positive k times is at least 1/2?