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10 couples go to a party (So 20 people in total). Each of the 20 people...

10 couples go to a party (So 20 people in total). Each of the 20 people are randomly seated at a large round table with 20 chairs. Let Xi = 1, for i = 1, 2, . . . , 20, if the i th person is sitting next to the other person in their couple, and 0 otherwise. Let Y be the total number of people who are seated next to their partner. (Note that the Xi ’s all have the same distribution, but are not independent.)

(a) What is E[Xi ]?

(b) What is E[Y ]?

(c) What is Var[Xi ]?

(d) What is E[XiXj ], if the i th person and j th person are in the same couple?

(e) What is E[XiXj ], if the i th person and j th person are not in the same couple?

(f) What is Var[Y ]?

Math   Statistics-And-Probability   
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