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In a group there are 25 students. Suppose their birthdays are independent and they are distributed uniformly in the 12 months. Find the expected value of the number of months in they aren't birthdays.

I know that $p(X)=1/12$ but I don't know how find the expected value.

Peter G
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  • Are you also assuming that every month has the same number of days? – Jack D'Aurizio May 31 '16 at 20:48
  • Yes, i suppose that. But the problem considers only the number of months in the year – Peter G May 31 '16 at 20:50
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    Hint: Let $X_i$ be the indicator variable telling you if the $i^{th}$ month is not represented in the group. Compute $E[X_i]$ and then use the linearity of expectation. – lulu May 31 '16 at 20:52

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