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Exercise 3. A random sample of 20 subjects with sickle cell anemia of African ancestry was genotyped at a locus in chromosome 2 that is supposed to be associated with less severe disease. The data summary is We wish to estimate the prevalence of carriers of one or more alleles B (hence genotype AB or BB ) in the population of sickle cell anemia patients of African ancestry. A priori, we assume that the prevalence of carriers of one or more alleles B is approximately 20%, based on data from 10 sickle cell anemia subjects of African ancestry. a. Describe a Bayesian Beta-Binomial model that could be used to describe the data, and describe a prior distribution that represents the prior knowledge. b. Compute the Bayesian estimate of the prevalence of carriers in sickle cell anemia patients of African ancestry. 1 BS849 - Bayesian Modeling for Biomedical Research \& Public Health Spring 2023 c. Estimate the probability that in a sample of 100 sickle cell anemia patients of African ancestry more than 50 will be carriers of one or more alleles B. d. Estimate the probability that in a sample of 100 sickle cell anemia patients of African ancestry the number of carriers of one or more alleles B is more than 30 but less than 70. NB. You can either use conjugate analysis or conduct your calculations using rjags