All Questions
2
questions
1
vote
1
answer
90
views
Probabilistic vs Geometric Theory of Integration
Motivating Question: Let $X$,$Y$ be independent standard uniform random variables. How does one show, rigorously, that
$$
\mathbb{E}[X \mid X+Y = 1] = \frac{1}{2}?
$$
I would be interested in hearing ...
- 1,003
1
vote
1
answer
661
views
Stereographic Projection of Uniform Distribution on Sphere
Consider a (punctured) unit sphere $S = \{ (x,y,z) \mid x^2+y^2+z^2 = 1, z\neq 1 \} $ and the plane $L = \{ (X,Y,0) \}$ (let us use the shorthand $(X,Y)$ for $(X,Y,0)$).
We can define the ...
- 16.7k