please solve this question

10. Maximum Likelihood and Maximum A Posteriori [11 points] Your company has developed a test for COVID-19. The test has a false positive rate of a, and a false negative rate of B. (a) [2 points] Assume that COVID-19 is evenly distributed through the population, and that the prevalence of the disease is y. What is the accuracy of your test on the general population? (b) [2 points] Your company conducts a clinical trial. They find n people, all of whom they know have COVID. What is the likelihood that your test makes n't correct predictions? (c) [5 points] Derive the maximum likelihood estimate for B. You may assume all other parameters are fixed. (d) [4 points] Derive the MAP estimate for , assuming it has a prior P(S) = Beta(a, b). You may assume all other parameters are fixed