All Questions
Tagged with geometric-probability conditional-probability
22
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Probability of two geometric conditions happening together
I have a problem combining geometry with probability, and I feel like I do not understand the basics to approach this problem.
Let there be two points $\mathbf{p}_1$ and $\mathbf{p}_2$ in $\mathbb{R}^...
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1
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Expected number of packs until two cards are collected
Say we want to collect two cards A and B, each appearing independently in the pack with probability $p$. Note that a pack may contain both A and B at the same time with probability $p^2$. I want to ...
- 33
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51
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Conditional probability, two vector valued RVs on a circle.
Given two vector valued RVs $ X,Y \in S_1$ (the unit circle) that are uniformly distributed. We choose a fixed vector $a \in S_1$, e.g. in x-direction: $a=e_x$.
We then sample once from both ...
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4
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Calculate expected number of heads in 10+$\xi$ coin tosses (GRE problem)
This is a problem from a preparatory GRE preparatory GRE test made by guys form University of Chicago.
Problem:
A man flips $10$ coins. With $H$ the number of heads, and $T$ the number of tails, the ...
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What is the probability of an angle to be obtuse in a triangle (presumed to be on a plane rather than curved surface)?
Here's the progress I (think I) have made.
EQUILATERAL TRIANGLES
For Equilateral triangles, the probability is zero for any angle.
ISOSCELES TRIANGLES
For Isosceles triangles, when defining one of the ...
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1
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1
answer
173
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Find CDF of minimum dependent identical distributed random variables
I'm a post-graduate researcher in Telecommunications and am currently studying Geogeomatric stochastic's applications.
In the process of building systems, I faced the challenge of finding the minimum ...
- 73
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1
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258
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a vague step in the proof of variance of geometric distribution
I've been reading a probability textbook recently and get stuck by the following steps in a proof of variance of geometric random variable, the idea is to use formula:$Var(X)=E[X^2]−E[X]^2$, $E[X]$ on ...
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Distribution of the number of elements of a random unit vector that exceed some value
I have been puzzling for a while on a problem that I managed to reduce to the following question.
Suppose that we have a real random $n$-vector $X$ that is uniformly distributed on the unit sphere in ...
- 41
2
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1
answer
80
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Combining probability density funciton and probability mass function
I was working on this problem:
...
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1
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Why are we not multiplying 1/n conditional probability of selecting disjoint points in the question - "prob. of N points within a semi-circle"
This is my first question on stackexchange - so apologies in advance if I haven't been able to follow the best practices while asking this question.
I am trying to understand the solution to question &...
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Probability of $-\frac{1}{4}\leq \sin (a x)\leq \frac{1}{2}$? [closed]
We know that probability of having $ \sin (a x)>0$ for a random $x$ is $\frac{1}{2}$.
Can we say something about the probability of the following condition?
$$-\frac{1}{4}\leq \sin (a x)\leq \frac{...
user868713
0
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1
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110
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Probabilistic geometric problem in high dimensions
In the $n$-dimensional Euclidean space, let $H$ be a random hyperplane selected in way similar to the so called "random radial point" (used to propose a solution for the Bertrand paradox): ...
- 149
2
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1
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259
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Geometric probabilistic problem on a plane
Let $T$ be a triangle with vertices belonging to a given Cartesian plane $P$ and with side lengths $a$, $b$ and $c$, where $a\ge b\ge c\ge 0$. Let $L_T$ be a straight line selected uniformly at random ...
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Count of random points belonging to a Voronoi cell in the unit square
I am considering a Voronoi tessellation in the unit square $V \in [0,1]^2$ for $G$ points uniformly randomly distributed. Then I am considering $N$ other points also randomly distributed uniformly in $...
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3
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Find the probability that a stick will lie entirely on the tile.
A floor is paved with tiles, each tile being a parallelogram such that the distance between pairs of opposite sides are $a$ and $b$ respectively, the length of diagonal being $L$. A stick of length $C$...
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