I Wish I Had More Friends

A well known probability problem is the birthday paradox; if you get over 23 people in a room, the odds are favorable that two people will share the same birthday.  I believe this is when the sample distribution moves to a population distribution.  That’s not my point.  My point is that I wish I had more friends.

Exploding with social popularity, Facebook always lets me know when my friends’ birthdays are.  Every few days I have a friend with a birthday, and that person’s received comments greatly increase that day.

Then my curiosity wandered: how many friends do I need to have in order to add a daily task of wishing someone a happy birthday? I used the lazy man’s approach: I avoided theory and just simulated. I used a uniform distribution for birthday odds. I continued the simulation until all of the 365 days were full, which I repeated a thousand times.

True story

The upshot of this: you need 1900 to 2800 friends before you can feel any confidence that you can add the daily task of “wishing happy birthdays” in your virtual community.

Maybe by the time I have that many friends I’ll know a more elegant theoretical solution.


1 Response so far »

  1. 1

    Interestingly, this came up on Twitter yesterday: http://www.psychologytoday.com/blog/the-scientific-fundamentalist/200911/why-your-friends-have-more-friends-you-do (“Why Your Friends Have More Friends than You Do”
    I haven’t taken a math class since honors whateveritwas in high school, so you’ll probably find this easier to understand than I do, but still: interesting.

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