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Puzzle for you guys. There are 20 people in a room. Assuming no one was born on a leap year, what is the variance of the number of pairs people who share a birthday. To be clear, if 3 people were born on christmas and 2 people were born on st patricks, this is considered to be 4 pairs of people who share a birthday.
Variance is defined as E[X^2] - E[X]^2, where E[X] is the expected number of pairs of people who share a birthday. So finding E[X^2] and E[X], where the random variable X is the number of pairs of people who share a birthday, yields the desired quantity.
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>>8739452
What is the distribution of birth dates? Should it be uniform across all dates except leap day?
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>>8739510
yes
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There should be 1-3 pairs
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>>8739711
1-3 pairs for what? i dont understand
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this was a homework problem for the introduction to probability class I took at MIT last semester
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>>8739741
of matching birthdays
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>>8740218
That is not the expectation or variance. Both of these are single numbers
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Expectation is defined as the sum of the product of the value of the random variable X and the probability of it taking that certain value over all possible values. For example let the random variable X be the number that comes up in a dice roll. E[X] = 1/6*1 + 1/6*2 ... + 1/6*6 = 3.5, as one would guess.
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