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Three restaurants provide dinner for 100 students. They served,
respectively, 20, 30 and 50 students. One of the students is randomly
selected. Let X denotes the number of students that have dinner at the
same restaurant with this randomly selected student. One of the 3
restaurants is also randomly selected. Let Y denotes the number of
students that have dinner at this randomly selected restaurant.
(a) Compute E[X] and E[Y ]. (10%)
(b) Compute Var[X] and Var[Y ] . (10%)

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