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Results tagged with geometric-probability
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user 48831
4
votes
Expected absolute value of the average of two points from the disc
(Too long for a comment)
For the record:
$$\mathrm{exp\_abs}(3)=\frac{4}{3 \pi^2}\,I_3=0.3671989447$$
where
$$I_3=\int_{-1}^1\int_{-1}^1 \int_{-1}^1 |x+y+z|\sqrt{1-x^2}\sqrt{1-y^2}\sqrt{1-z^2}\,dx\,dy …
- 3,255
5
votes
Average distance of the mean of $n$ random complex numbers in a unit disc
Here is another method.
Since the uniform distribution on the unit disk is rotationally symmetric (invariant under orthogonal transformations), the problem can be reduced to a random walk problem in $ …
- 3,255
1
vote
Accepted
Total progeny of a Galton-Watson branching process - standard textbook question
The answer above is fine, nevertheless I make some hopefully useful supplementary remarks (the first two essentially reformulating Did's answer)
(1) It is well known (see e.g. Feller I, 3rd ed., p.29 …
- 3,255