1
vote
1answer
31 views

Probability of finding a point on or in an $n$-dimensional unit sphere

If a point is chosen at random in an $N$-dimensional unit sphere, what is the probability of falling inside the sphere of radius $0.99999999$? What if $N=3$, $N=10^{23}$, or $N = \infty $? Okay, that ...
4
votes
0answers
77 views

Clarification in a paper

This is regarding a clarification in page 384 of a paper published in Annals of Statistics by Amari. In page no. 384, he defines $$R_i(t)=\frac{\partial}{\partial \theta_i} ...
0
votes
1answer
38 views

Optimal $p$ for biased coin?

You are given a biased coin with probability $p$ of getting $H$ and $1-p$ of getting tail. Each flip is independent of another. We keep flipping the coin until we get $4$ consecutive tails. For each ...