1 results
The volume of a random simplex in an n-ball is asymptotically normal
-
- Journal:
- Journal of Applied Probability / Volume 14 / Issue 3 / September 1977
- Published online by Cambridge University Press:
- 14 July 2016, pp. 647-653
- Print publication:
- September 1977
-
- Article
- Export citation
-
A proof is given of a conjecture in the literature of geometrical probability that the r-content of the r-simplex whose r + 1 vertices are independent random points of which p are uniform in the interior and q uniform on the boundary of a unit n-ball (1 ≦ r ≦ n; 0 ≦ p, q ≦ r + 1, p + q = r + 1) is asymptotically normal (n →∞) with asymptotic mean and variance
and 
, respectively.
and 
, respectively.