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Complex normal distribution

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Square partition

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Two random points in [0,1]

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Factors and Multiples Puzzle

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Counting 1s

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 ...

Tags: statistics normal

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

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 ...

Tags: probability expectation

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 ...

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 ...