Many medial conditions are inherited as autosomal recessive traits (e.g., cystic fibrosis, sickle cell anemia, Tay-Sachs). Two recessive alleles are necessary for expression of the disease. Therefore, when each biological parent is a carrier (i.e., each parent has one copy of the allele), there is a one in four chance of transmitting the genetic condition to each offspring. a) Let Y represent the number of offspring affected in three children born to parents who are both carriers of cystic fibrosis. Is Y a binomial random variable? Explain your response. b) Let X represent the number of children conceived to a carrier couple before an affected offspring is encountered. Is X a binomial random variable? Explain. c) Suppose a couple who are both carriers of the cystic fibrosis allele plan to have 3 children. Build the probability mass function for the number of children that will have cystic fibrosis (i.e., the number that will receive the recessive allele from both parents). Y= number offspring with disease probability