Statistics

Test for TB TB absent TB present Negative 1739 8 Positive 51 22 Data for TB testing using Xray imaging Table shows the results of using X-ray imaging as a diagnostic test for tuberculosis in patients with known TB status. Use it to answer the questions below. 1. Calculate the marginal probabilities of the individual random variables, i.e. the probability of positive and negative Xray test results, and of TB being present and absent. 2. Find the probability of positive result given that TB is absent (false positive rate} and the probability of a negative result given that TB is absent {specicity}. 3. Find the probability of negative result given that TB is present (false negative rate) and the probability of a positive result given that TB is present {sensitivity}. 4. Find the probability that a person who tests positive actually has TB (probability of TB present given a positive result]. 5. Find the probability that a person who tests negative does not have TB (probability of no TB given a negative result). 6. Assuming the test result and the TB status are independent, calculate the expected probability of both TB being present and a positive Xray test} I". Under the same assumption, calculate the expected probability of both TB being absent and a positive Xray test