All Questions
5 questions
13
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762
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If $(a,b,c)$ are the sides of a triangle, then the probability $P(ax + by \ge c) = \frac{4}{\pi^2}\chi_2(x) + \frac{4}{\pi^2}\chi_2(y)$
Posting this question in MO since it is unanswered in MSE
Let $(a,b,c)$ be the side of a triangle. In its most general linear form, the triangle inequality can be expressed as: Does $ax + by \ge c$ ...
- 5,470
11
votes
1
answer
746
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Find the area of the region enclosed by $\sin^p x+\sin^p y=\sin^p(x+y)$, the $x$-axis and the $y$-axis (comes from a probability question)
Consider the graph of $\sin^p x+\sin^p y=\sin^p(x+y)$, where $x$ and $y$ are acute, and $p>1$.
Here are examples with, from left to right, $p=1.05,\space 1.25,\space 2,\space 4,\space 100$.
Find ...
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5
votes
1
answer
2k
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Normal multivariate orthant probabilities
(Previously I posted a similar question on math.SE, hoping that this question would have an easy answer. As the question appears hard, I am hoping I can perhaps get more feedback here.)
Let $\mathbf{...
- 733
1
vote
1
answer
241
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Integration by parts for indicator of a sphere to indicator of a ball
Broadly speaking, I have a radial distribution on $\mathbb R^n$, i.e., the pdf only depends on the $\ell_2$-norm of the argument. I would like to obtain an expression for the pdf in the form $\int_{w=...
0
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0
answers
454
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Reference: Bochner Integral`
What would be an easily accessible book dealing with Bochner integration as applied to probability theory (I'm looking to understand random elements and their basic related concepts in a formal yet ...
- 5,405