After your yearly checkup, the doctor has bad news and good news. The bad news is that you tested positive for a serious disease and that the test is 99% accurate (i.e., the probability of testing positive when you do have the disease is 0.99, as is the probability of testing negative when you don’t have the disease). The good news is that this is a rare disease, striking only 1 in l0, 000 people of your age. Why is it good news that the disease is rare? What are the chances that you actually have the disease?
Answer to relevant QuestionsShow that the statement P (A, B│C) = P (A│C) P (D│C) is equivalent to either of the statements P (A│B, C) = P (A│C) and P (B│A, C) = P (B│C).(Adapted from Pearl (1988)) Suppose you are a witness to a nighttime hit-and-run accident involving a taxi in Athens. All taxis in Athens are blue or green. You swear, under oath, that the taxi was blue. Extensive testing ...e. What is the most likely number of stars, given these observations? Explain how to compute this, or, if it is not possible to compute, explain what additional information is needed and how it would affect theresult.Three soccer teams A. B, and C, play each other once. Each match is between two (earns, and can be won, drawn, or lost. Each team has a fixed, unknown degree of quality— an integer ranging from 0 to 3—and the outcome of ...In this exercise, we analyze in more detail the persistent-failure model for the battery sensor in Figure (a). a. Figure (b) stops at t = 32. Describe qualitatively what should happen as t → ∞ if the sensor ...
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