1 Pfizer BioNTech COVID-19 vaccine trial Weill continue our analysis from Llominwork of the PIONOWED 19 cm Patrial data (inodified slightly for the purposes of this quiz Read that wubjects were randomly given either the vaccine or a placebo. The number of subjects in much group along with The munbem o COVID-19 es in each he end of the trial is kiven in the following tables group by Vaccine No Vaccine MILAN Total subjects COVID-19 casosi 17.411 17 611 162 8 022 270 As in Homework 3. we will modd the timber of COVID-19 cises in the vaccine group (8) As a realization of Y - Binem(s) where a 170 is the number of COVID-19 cases in the experiment. We would like to infer, which is Pr{recived vaccine Infceted with COVII-19} Ilcre, we'll take a Bayesian approach. (1) 1. Based on the results of Phase 1 and 2 trials, the prior for II osad in the Phase 3 study was Beta(0.700102, 1); the prior PDE is shown as the solid line below. Compared to a uniform prior PDP dashed line), does this reflect a belief that the vaccinc reduce increases, or has no effect on the chance of being infected with GOVID-197- Brielly explain your pasoning. 12 12 mark(s)] 2. Write an expression for the posterior PDF, Puji (Tu), up to a constant of proportionudity. That is, for Puirfly) og(y), what is the function gw, y), 3 mark(s)] 3. Based on the previous part, what is the posterior distribution of Il conditioned on Y 12 [2 mark(s)] 4. Find the 95% posterior credible interval for II, and include any R code you use ta find it. Please round your answers to four (4) decimal places, 13 marks) 5. The effectiveness of the Ynecine is clefined 118 1 1 It is straighatlarward to show that a %, which is a monotonie (deeressing) transformation 1. What is the 95% credible interval lor 07 (Please round ta four decimal places) b. What is the posterior probability that the vaccine is at least 90% atleetive. 19 e Re calculate the value and write the R code vou me to obtain the answer. Please round to four decimal placer.) # mark(s)] 1 Pfizer BioNTech COVID-19 vaccine trial Weill continue our analysis from Llominwork of the PIONOWED 19 cm Patrial data (inodified slightly for the purposes of this quiz Read that wubjects were randomly given either the vaccine or a placebo. The number of subjects in much group along with The munbem o COVID-19 es in each he end of the trial is kiven in the following tables group by Vaccine No Vaccine MILAN Total subjects COVID-19 casosi 17.411 17 611 162 8 022 270 As in Homework 3. we will modd the timber of COVID-19 cises in the vaccine group (8) As a realization of Y - Binem(s) where a 170 is the number of COVID-19 cases in the experiment. We would like to infer, which is Pr{recived vaccine Infceted with COVII-19} Ilcre, we'll take a Bayesian approach. (1) 1. Based on the results of Phase 1 and 2 trials, the prior for II osad in the Phase 3 study was Beta(0.700102, 1); the prior PDE is shown as the solid line below. Compared to a uniform prior PDP dashed line), does this reflect a belief that the vaccinc reduce increases, or has no effect on the chance of being infected with GOVID-197- Brielly explain your pasoning. 12 12 mark(s)] 2. Write an expression for the posterior PDF, Puji (Tu), up to a constant of proportionudity. That is, for Puirfly) og(y), what is the function gw, y), 3 mark(s)] 3. Based on the previous part, what is the posterior distribution of Il conditioned on Y 12 [2 mark(s)] 4. Find the 95% posterior credible interval for II, and include any R code you use ta find it. Please round your answers to four (4) decimal places, 13 marks) 5. The effectiveness of the Ynecine is clefined 118 1 1 It is straighatlarward to show that a %, which is a monotonie (deeressing) transformation 1. What is the 95% credible interval lor 07 (Please round ta four decimal places) b. What is the posterior probability that the vaccine is at least 90% atleetive. 19 e Re calculate the value and write the R code vou me to obtain the answer. Please round to four decimal placer.) # mark(s)]