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Question: Fred decides to take a series of n tests, to diagnose whether he has a certain disease (any individual test is not perfectly reliable, so he hopes to reduce his uncertainty by taking multiple tests). Let D be the event that he has the disease, p = P(D) be the prior probability that he has the disease, and q = 1-p. Let Tj be the event that he tests positive on the jth test.
(a) Assume for this part that the test results are conditionally independent given Fred's disease status. Let a = P(Tj|D) and b = P(Tj|Dc), where a and b don't depend on j. Find the posterior probability that Fred has the disease, given that he tests positive on all n of the n tests.
(b) Suppose that Fred tests positive on all n tests. However, some people have a certain gene that makes them always test positive. Let G be the event that Fred has the gene. Assume that P(G) = 1/2 and that D and G are independent. If Fred does not have the gene, then the test results are conditionally independent given his disease status. Let a0 = P(Tj|D,Gc) and b0 = P(Tj|Dc,Gc), where a0 and b0 don't depend on j. Find the posterior probability that Fred has the disease, given that he tests positive on all n of the tests.
Perform the significance test that compares the model dress for the three categories of magazine readership. Summarize the data numerically and graphically
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ESPN reported in sample of 1000 homes the proportion of people who watched the Texas v. Ohio State college football game this weekend was .6.
consider the question what is the probability of getting a 6-card poker hand that contains a card from all four suits
Hugh's Repair Shop specializes in repairing German and Japanese cars. The shop has two mechanics. One mechanic works on only German cars and the other mechanic works on only Japanese cars.
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Two members of the department of philosophy (Locke and Kant) were responsible for hiring a new professor. Each privately ranked from 1 to 10 the ten candidates.
If we have 25 bivariate observations and FX,Y is bivariate normal with correlation coefficient .3, what is the approximate power of the level α = .045 test of H0 (8.1) versus the alternative τ > 0?
Suppose 80% of kids who visit a doctor have a fever, and 20% of kids with a fever have a sore throats. What's the probability that a kid who goes to the doctor has a fever and a sore throat?
Using the critical-value approach and the 1% significance level, can you conclude that the mean daily (liquid) water consumption by this population differs.
sokal and rohlf 1981 studied purebred canadian dairy cattle. the butterfat percentages from 2-year-old cows follow a
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