# A Mathematician’s Lament

# Expected number of different birthdays

(one)Birthday problem!

Jack's Personal Blog on Mathematics

Suppose there are *n* people in a room. It is the well known ‘birthday problem‘ that if *n > 22* the probability of two people sharing the same birthday is greater than 50%, and so it is very likely that there aren’t *n* unique birthdays. However, what is the *expected* number of unique birthdays?

[Let us assume there are *D* days in a year, in order to be more general.]

Actually, the expected number of unique birthdays is very easy to calculate. Let *e(n)* denote the expected number of unique birthdays when there are *n* people.

Choose one of the *n* people. Then either they have a different birthday than everybody else, or they don’t. They have a different birthday than the other *n-1* with probability $latex left(frac{D-1}{D}right)^{n-1}&bg=ffffff$. Let us write $latex phi&bg=ffffff$ for $latex (frac{D-1}{D})&bg=ffffff$, and so the probability that they have a different birthday to everybody…

View original post 770 more words

# A Chronology of Game Theory by Paul Walker

# Fourier transform for dummies

# Convolution of compactly supported function with a locally integrable function is continuous?

# Example of two functions that are equal almost everywhere?

# love it!

# A Stochastic Game without a Stationary Discounted Equilibrium

# quals exam 13 Fall@Harvard

After this you never study for a grade…which we shouldn’t at the first place.