Task 2: Assume you are tested for a disease called conditionitis, a medical condition that you believe afflicts a proportion p of the population, with you modelling p as being beta distributed with parameters" = 1.41 and B = 547.12. The test result is positive, i.e., the test claims that you have the disease. You immediately perform a second, independent test. The first test is a conditionitis Antigen Rapid Test (Oral Fluid) and its clinical performance is given as: PCR confirmed sample number Correct identified Rate Positive sample 101 91 90.1% (Sensitivity) Negative sample 305 303 99.3% (Specificity) Total 406 394 97.0% (Total Accuracy) The second test is a conditionitis Antigen Rapid Test (Nasal Swab) and its clinical performance is given as: PCR confirmed sample number Correct identified Rate Positive sample 311 291 93.6% (Sensitivity) Negative sample 763 763 99.9% (Specificity) Total 1074 1054 98.1% (Total Accuracy) Analyse these data and answer the following questions: 1. Which priors did you use in your modelling of the sensitivity and the specificity of each test? 2. What is the probability that you have conditionitis if the first test comes back positive? 3. What is the probability that you have conditionitis if the second test comes back positive too? 4. What is the probability that you have conditionitis if the second test comes back negative (after the first test came back positive)? 5. You realise that the two tests are produced by the same company. Do you think that the assumption that the results of the two tests given your (unknown) disease status are independent is tenable? Comment briefly