Let X be a gene that is known to inuence eye colour. Whether this gene occurs in variation 0, 1, or 2 has an inuence on the eye colour of an individual. We are interested to nd out about the probability of an individual having brown eyes (Y = 0) or not (Y = 1). If an individual has variation 0 of the gene, it has brown eyes (Y = 0) with probability 0.9. The probability of an individual to not have brown eyes if variation 0 is present is 0.1. If variation 1 of the gene is present, the probability of having brown eyes is 0.5, and if variation 2 of the gene is present, the probability of having brown eyes is 0.2. The probability of having gene variation 0 is 0.8, and for variation 1 it is 0.1. (a) Give the probability mass function for Y