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HW 6

HW 6. 1. Voters often change their party affiliation is subsequent election. In a certain district republicans remain republicans for the next election with probability 0.9, while Democrats stay with their party with p = 0.8. Describe this process and find the asymptotic distribution. .

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HW 6

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  1. HW 6

  2. 1. Voters often change their party affiliation is subsequent election. In a certain district republicans remain republicans for the next election with probability 0.9, while Democrats stay with their party with p = 0.8. Describe this process and find the asymptotic distribution.

  3. 2. Four out of every five tracks on the road is followed by a car, while one out of every six cars is followed b a truck. What proportion of vehicles on the road are tracks? Hint: t - share of tucks on the road;c - share of cars;p(a,b)- transition probability for a -> b (see the table)

  4. 3. You are about to have an interview for Harvard Law school. 60% of the interviewers are liberals and 40% are conservatives. 50% of conservatives smoke cigars but only 25% liberals do. The interview lights up a cigar. What is the probability that he is liberal?

  5. 4. Suppose for simplicity that number of children in a family is 1 , 2 or 3 with probability 1/3 each. Little Bobby has no sisters. What is the probability that he is the only child? Hint: the statement that Bob is the only child means that (a) there is only one child and (b) that this child is a boy.

  6. 5. D. Plumber Bob does 40% of the plumbing jobs in a town. 30% of people in town are unhappy with their plumbers but 50% of Bob’s customers are unhappy with his work. If your neighbor is unhappy with his plumber, what is the probability it was Bob?

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