Questions tagged [set-theory]

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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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Meaning of set notation applied in time series analysis proof

Let $\{ Y_{t}\}$ be a stationary process with autocovariance function $\gamma_{k}$. Let $\bar{Y} = \frac{1}{n}\sum_{t = 1}^{n}Y_{t}$. Show that: $Var(\bar{Y}) = \frac{\gamma_{0}}{n} + \frac{2}{n} \...
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The actual framework of population / sample random variables, parameters and associated distributions

I am thinking through the relation among population and sample random variables, the parameters describing them, and distribution functions. Random variables are functions quantifying real events, ie ...
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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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