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Complex normal distribution

x and y are iid normal random variables with zero mean and variance a^2. Define r and q as follows:

r=(x^2-y^2)/sqrt(x^2+y^2),
q=2xy/sqrt(x^2+y^2),

Compute the joint pdf of r ...


Square partition

Can you partition a square into an odd number of triangles of equal area?


Two random points in [0,1]

Two i.i.d uniform random points x and y on the interval [0,1] result in three segments summing to 1.

(1) What is the expected length of the shortest ...


Factors and Multiples Puzzle

http://www.interactivemaths.net/node/164

Starting with a 100 Grid, the first player chooses a positive even number that is less than 50, and crosses it out on the grid. The second player ...

Tags: number puzzle

Counting 1s

Consider a function which, for a given whole number n, returns the number of 1s required when writing out all numbers between 0 and n.

For example, f(13)=6. Notice ...

Tags: google number