13. There are 25 students in a probability class. What is the expected number of birthdays that...

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13. There are 25 students in a probability class. What is the expected number of birthdays that belong only to one student? Assume that the birthrates are constant throughout the year and that each year has 365 days. Hint: Let Xi = 1 if the birthday of the ith student is not the birthday of any other student, and Xi = 0, otherwise. Find E(X1 + X2 + · · · + X25).

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