Questions tagged [set-theory]
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11
questions
2
votes
1answer
78 views
How to implement conditional probability distribution on set-valued Random variables?
A Random Set is a set-valued RV, i.e. a map $X:\Omega\to\mathcal{C}$ from a probability space $(\Omega,\Lambda,P)$ to the family of measurable closed sets $\mathcal{C}$ on a $\sigma-$algebra $\Lambda$ ...
3
votes
2answers
95 views
Intuition - Uncountable sum of zeros
I am reading the Probability Lifesaver and in the introduction to continuous variables it shows the contradiction when summing infinite number of zeros such as the union of signleton events as,
I can ...
0
votes
2answers
71 views
statistical method for finding significant numbers in a set [closed]
Suppose that we have a population of $N= 1000$ people and they want to select 5 items (for simplicity) $\{A, B, C, D, E\}$ (but actually number of items is in the order of thousands). Number of ...
0
votes
1answer
23 views
Difference between outcome space and sample space
I have 26 tiles each one with a different letter of the English alphabet: $A, B, C,...,Z.$
I draw two tiles with replacement.
The possible outcomes are: $$S=\{AA, AB, AC,..., AZ, BA,...,ZZ\},$$ which ...
3
votes
1answer
36 views
When to stop enumerating a set of unknown cardinality via random sampling?
DNS resolution can sometimes return one of multiple IP addresses, for load balancing. I would like to enumerate a list of IPs for a service so I can whitelist traffic to a domain without performing an ...
0
votes
1answer
40 views
$\inf$ of a sequcence of random variables bigger than some $a\in\mathbb{R}$
Suppose we have sequence of random variables $\{X_n\mid n\in\mathbb{N}\}$, defined on a probablity space $(\Omega,\mathcal{F},\mathbb{P})$. Then we define $(\inf_{n\in\mathbb{N}}X_n)(\omega)=\inf_{n\...
1
vote
0answers
18 views
Wisdom of the Crowd Disagreement Probability [closed]
I'm trying to estimate the likelihood that a set of annotators will have at least one dissenter. For n annotations, we know the probability that they will annotate any given record P(a) and the ...
0
votes
0answers
8 views
Multi-categorical set balancing
I have a particular mathematical problem that I would name as multi-categorical set balancing. I don't think this is a new problem but I do not know the correct term for it, therefore I am also ...
2
votes
2answers
1k views
What is the variance of the difference of two random-variable indicators with a chance of intersection between events?
Let $X$ be an event whose probability P($X$) = $p$ and let $Y$ be an event whose probability is P($Y$) = $q$. The probabilit$Y$ of $X$ intersection with $Y$, $P(X \cap Y)$ = $r$.
$I_X$ is the ...
1
vote
3answers
63 views
probability of the union and intersection of sets A and B
If I have two sets A and B and take
$$ P((A\cap B) \cap (A\cup B)),$$
is this the same as $P(A\cup B)$?
0
votes
1answer
57 views
Union of intersection of B and A and intersection of B and A complementation
Due to my little knowledge in set theory, I simply don't know how the authors of Statistical Inference could make this highlighted statement
Could someone please explain? What book should I read to ...
