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Question 1 Despite assumptions to the contrary, it is possible to test positive using a PCR test, and be diagnosed as having Covid-24, even if someone has not been infected with SARS-Cov-4 and has no symptoms of the disease. The government's policy recommendation is that people testing positive should self isolate for 10 days. A number of factors might influence the reliability of the PCR test such as cross reactivity with other viruses, lab mix-ups and faulty/non- sterile testing equipment. a) Calculate the posterior probability of a random person, with no Covid-24 symptoms, actually having SARS-Cov-4, P(SARS-Cov-4 = True, PCT Test = positive), given the following information P(SARS-Cov-4 = True) = 0.02 P(PCR Test = Positive | SARS-Cov-4 = True) = 0.9 P(PCR Test = Positive | SARS-Cov-4 = False) = 0.2 b) Calculate the marginal probability of a false positive result P(False positive = Yes | PCR Test, SARS-Cov-4) c) Use the Binomial distribution to calculate the number of false positives, f, in the population, where p = P(False positive = Yes | PCR Test, SARS-Cov-4). t-Binomial (p,n = 50 milion) d) What would the implications of random SARS-Cov-4 screening be on the self- isolation rate in an adult population of 50 million people subject to such screening

Question 1 Despite assumptions to the contrary, it is possible to test positive using a PCR test, and be diagnosed as having Covid-24, even if someone has not been infected with SARS-Cov-4 and has no symptoms of the disease. The government's policy recommendation is that people testing positive should self isolate for 10 days. A number of factors might influence the reliability of the PCR test such as cross reactivity with other viruses, lab mix-ups and faulty/non- sterile testing equipment. a) Calculate the posterior probability of a random person, with no Covid-24 symptoms, actually having SARS-Cov-4, P(SARS-Cov-4 = True, PCT Test = positive), given the following information P(SARS-Cov-4 = True) = 0.02 P(PCR Test = Positive | SARS-Cov-4 = True) = 0.9 P(PCR Test = Positive | SARS-Cov-4 = False) = 0.2 b) Calculate the marginal probability of a false positive result P(False positive = Yes | PCR Test, SARS-Cov-4) c) Use the Binomial distribution to calculate the number of false positives, f, in the population, where p = P(False positive = Yes | PCR Test, SARS-Cov-4). t-Binomial (p,n = 50 milion) d) What would the implications of random SARS-Cov-4 screening be on the self- isolation rate in an adult population of 50 million people subject to such screening

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question 1 Despite assumptions to the contrary, it is possible to test positive using a PCR test, and be diagnosed as having Covid-24, even if someone has not been infected with SARS-Cov-4 and has no symptoms of the disease. The government's policy recommendation is that people testing positive should self isolate for 10 days. A number of factors might influence the reliability of the PCR test such as cross reactivity with other viruses, lab mix-ups and faulty/non- sterile testing equipment. a) Calculate the posterior probability of a random person, with no Covid-24 symptoms, actually having SARS-Cov-4, P(SARS-Cov-4 = True, PCT Test = positive), given the following information P(SARS-Cov-4 = True) = 0.02 P(PCR Test = Positive | SARS-Cov-4 = True) = 0.9 P(PCR Test = Positive | SARS-Cov-4 = False) = 0.2 b) Calculate the marginal probability of a false positive result P(False positive = Yes | PCR Test, SARS-Cov-4) c) Use the Binomial distribution to calculate the number of false positives, f, in the population, where p = P(False positive = Yes | PCR Test, SARS-Cov-4). t-Binomial (p,n = 50 milion) d) What would the implications of random SARS-Cov-4 screening be on the self- isolation rate in an adult population of 50 million people subject to such screening
Transcribed Image Text:Question 1 Despite assumptions to the contrary, it is possible to test positive using a PCR test, and be diagnosed as having Covid-24, even if someone has not been infected with SARS-Cov-4 and has no symptoms of the disease. The government's policy recommendation is that people testing positive should self isolate for 10 days. A number of factors might influence the reliability of the PCR test such as cross reactivity with other viruses, lab mix-ups and faulty/non- sterile testing equipment. a) Calculate the posterior probability of a random person, with no Covid-24 symptoms, actually having SARS-Cov-4, P(SARS-Cov-4 = True, PCT Test = positive), given the following information P(SARS-Cov-4 = True) = 0.02 P(PCR Test = Positive | SARS-Cov-4 = True) = 0.9 P(PCR Test = Positive | SARS-Cov-4 = False) = 0.2 b) Calculate the marginal probability of a false positive result P(False positive = Yes | PCR Test, SARS-Cov-4) c) Use the Binomial distribution to calculate the number of false positives, f, in the population, where p = P(False positive = Yes | PCR Test, SARS-Cov-4). t-Binomial (p,n = 50 milion) d) What would the implications of random SARS-Cov-4 screening be on the self- isolation rate in an adult population of 50 million people subject to such screening
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