2. Let us consider two independent generations of families, each generation comprising 5 in- dividuals. Let...

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2. Let us consider two independent generations of families, each generation comprising 5 in- dividuals. Let X be a random individual chosen from generation 1, with the eldest coded as 1, second coded as 2, etc. (so takes values 1, 2, ..., 5, with equal probabilities). Let Y be an individual belonging to generation 2 comprising 6 individuals of which two are twins (again represented as an integer between 1 and 5). (a) (3 pts) Do X and Y have the same distribution? Why or why not? Hint: Think of the PMFs of X and Y. (b) (3 pts) What is P(X + Y = 3)? 2. Let us consider two independent generations of families, each generation comprising 5 in- dividuals. Let X be a random individual chosen from generation 1, with the eldest coded as 1, second coded as 2, etc. (so takes values 1, 2, ..., 5, with equal probabilities). Let Y be an individual belonging to generation 2 comprising 6 individuals of which two are twins (again represented as an integer between 1 and 5). (a) (3 pts) Do X and Y have the same distribution? Why or why not? Hint: Think of the PMFs of X and Y. (b) (3 pts) What is P(X + Y = 3)?