Questions tagged [set-theory]
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16 questions
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Why is the square of the average of a set of positive numbers not always bigger than the average of the squares of the same set of positive numbers?
Why is the square of the average of a set of positive numbers not always bigger than the average of the squares of the same set of positive numbers?
I am not talking about in an asymptotic case.
user263327
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What does $\times_i \Sigma_i$ mean?
I cannot for the life of me figure this out. The context is from game theory (source: Game Theory by Fudenberg, Tirole):
... the space of mixed strategy profiles is denoted $\Sigma = \times_i \...
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Why is the number of subsets in a sample space $2^n$?
I am working my way through the statistical inference textbook and am stuck on this question:
Suppose that a sample space $S$ has $n$ elements. Prove that the
number of subsets that can be formed ...
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What is the difference between the alphabet set and the support of a random variable?
I'm having trouble identifying the differences between the two. Are they equivalent? Here's the definitions from http://www.stat.yale.edu/~yw562/teaching/itlectures.pdf
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Probability, set theory and predicates
If $P(t_1,\ldots,t_{n+m})$ is some predicate depending on $n+m$ terms (for example $x\leq c$ depends on two terms), and each $X_i$ is a discrete random variable with support $\Omega_i$, and each $c_i$ ...
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Event space of compound events
I have a pile of coloured cards in a box containing 2 blue, 2 red and 2 yellow cards.
My experiment consists of taking two cards from the box with replacement.
I'm pretty sure the sample space is all ...
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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 $\Lambda$ ...
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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 ...
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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 ...
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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 ...
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When to stop enumerating a fixed 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 ...
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$\inf$ 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\...
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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 ...
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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 ...
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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 $P(A\cup B)$?
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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 ...
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