# Tagged Questions

272 views

### Why is a random variable called so despite being a function?

According to my knowledge, its a function $P(X)$ which includes all the possible outcomes a random event.
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### If $X$ is distributed normally with mean $0$, is it correct to say $X$ and $-X$ “have the same distribution”?

Q: If $X$ is distributed normally with mean $0$, is it correct to say $X$ and $-X$ have the same distribution? In a way, this seems correct: both $X$ and $-X$ have the same probability density ...
21 views

### Standard deviation and related quantities

By definition, standard deviation is the square root of the variance. There is some common terminology for the quantities $$\mathbb{E}(|X-\mathbb{E}X|^p)^{1/p}$$ for $p \geq 1$? Or, they are just ...
29 views

### Mean squared [X] or Mean [X] squared?

If I have two functions, as below, which one is "Mean [X] squared" and which is "Mean squared [X]"? Would I be correct in saying the former is number 1 and the latter is number 2? Thanks in advance ...
35 views

### What does a probability being i.i.d means?

I know that a sequence of random variables is i.i.d means that they have the same mutually independent probability distribution. I was reading in a paper where the authors said that "the probability ...
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### Is there a name for the trivial probability distribution P(X=x) = 1 for a unique x?

Is there a name for the trivial probability distribution given by $P(X=x) = 1$ for a unique $x$ and $P(X=y) = 0$ for all $y \ne x$? I know it is very trivial, but since it is the distribution that ...
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### What's the name of the quantity $\mathbb{P}(A\cap B)/(\mathbb{P}(A)\mathbb{P}(B))\;$?

In a physics book, I've come across the quantity $$\frac{\def\P{\mathbb{P}}\P(A\cap B)}{\P(A)\P(B)}\,,$$ where $A$ and $B$ are events. The author calls this quantity the correlation of $A$ and ...
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### Terminology for 'clusters' in a discrete probability distribution?

I have attached an image of a probability distribution. As you can see their are peaks, and in my opinion thee 'clusters' in this distribution. There is the cluster that spans the origin and goes out ...
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### Name of decision method in which probability of taking an action is exactly past successes / past attempts, while alternative actions normalize

The probability of choosing among options $X_1$, $X_2$, $X_3$, $...X_n$ is initially uniform, i.e. $P(X_j)=1/n$. On choosing $X_j$, either success or failure will occur (with unknown probabilities, ...
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### What's the meaning of the term RECALL in information retrieval?

From the wiki of Precision and recall: recall (also known as sensitivity) is the fraction of relevant instances that are retrieved. I can understand the literal meaning of "sensitivity", but ...
223 views

### Probability of a Min/Max

I am studying probability for an exam and I am finding hard to understand the notion of $P(\min(X_1,X_2))$ and $P(\max(X_1,X_2))$, where $X$ is a discrete or a continuous variable. I have found in my ...
42 views

### Analytic methods vs Monte Carlo (terminology)

What's the correct terminology to say "We can calculate the probability exactly using pure math, as opposed to Monte Carlo simulation"? Analytically sounds like we need Calculus, which we may not ...
103 views

### Formal Mathematical Terminology For Tree Diagrams

I currently have a tree diagram that shows the probabilities for certain paths in a game. The tree diagram first branches into four possibilities and then another four possibilities for each of the ...
103 views

### Is the mathematical concept of an “operation” necessarily deterministic?

Does the mathematical concept of an operation require that the process is deterministic? If not, what are some example cases for non-deterministic operations? Motivation: I am coming from a ...
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### What is a two point support in this lemma?

What is the terminology of two point support in this lemma?
134 views

### Birthday paradox: meaning of random

In the wikipedia page (http://en.wikipedia.org/wiki/Birthday_problem) on birthday paradox the following statement has been said : "the probability that, in a set of $n$ "randomly chosen" people, some ...
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### a random process model which I do not know the name of

My friend explained to me the following model which comes psychology. I am fairly certain there must be mathematicians who study this type of thing because on its own right it is a very interesting ...
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### What does multilinear function mean?

A draft research paper claims that $Q(p)=1-p_1 p_2 p_3 p_4 - p_2 p_3 p_6 p_7-p_1p_2$ is multilinear where $p_i = \mathbb P(e_i)$ and $e_i$ is a basic event of a component to fail. I have learnt in LP ...
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### Complement and Negation: $P(A)=0\rightarrow P(\neg A)=1$?

My earlier question became too long so succintly: Suppose $P(C)=0.2$. Its complement is 0.8 i.e. $P(C)^C=0.8$ but what does $P(¬C)$ mean? I think I am messing up the term complement and negation? ...
185 views

### Probability distribution functions: factorization 3-way implies 2-way?

I recently asked a question about pairwise versus mutual independence (also related to this and this q). However, (1) I inadvertently used incorrect terminology: three events, A, B, C are ...
133 views

### Negatively Correlated Events

I showed the following inequality to a colleague, where $A$ and the $B_i$ are all events: $$\Pr\left(A \mid \bigwedge_{i = 1}^n \overline{B_i} \right) \leq \Pr(A)$$ He summarized, "So $A$ is ...
1k views

### How do I read this distribution function: $\min(X,Y)$?

I'm confused on what the $\min$ means. For example if I need to find the distribution function of $\min(X,Y)$ what am I looking for exactly? Am I looking for the distribution of the minimum value of ...
33 views

### Name for maximum transition probability

Let $p(x,y)$ denote the transition probability of a markov chain. Similarly, let $p^n(x,y)$ be the n-step transition probability. My question is, is there a formal name for $S(x,y):=\sup_n p^n(x,y)$. ...
483 views

### Do hashing functions have a probability distribution calculated for their output?

This question might look strange, so I will try to be clear. Consider a hashing function $f : M \mapsto H$ which takes a message with arbitrary length $m \in M$ as input and returns a hash $h \in H$ ...
255 views

### What is this operation on random variables called?

Let $X$ be a random variable and let $N$ be a discrete random variable which takes values in the non-negative integers. Let $X_1, X_2, ...$ be a sequence of i.i.d. random variables with the same ...
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### Modifying a discrete probability distribution according to set of weights

Given a discrete probability distribution (e.g., ${P_1=0.85,P_2=0.05,P_3=0.05,P_4=0.05}$), I would like to transform it according to some set of "weights" (say, ${w_1=2,w_2=0.5,w_3=1,w_4=0.5}$), which ...
156 views

### Sorting through “algebra of random variables,” vs. “probability space,” etc

I have been reading through Wikipedia pages, and I'm still really confused. What is the difference between "algebra of random variables" and "probability space."? Are they just different words for ...
983 views

### name for a rational number between zero and one?

I'm searching for a unified name to convey for the concept that a number will always be between zero and one. Some info for context: in probability we've got a number between 0 and 1. Percentages ...
267 views

### probability terminology for parameter in a Markov process

Suppose $$P(\text{feature present at time} \ t \ \text{and} \ t+\Delta t) = \beta^{2}+\beta(1-\beta) \exp(\Delta t/\tau)$$ where $\tau = 1/(\pi_{01}+\pi_{10})$. What is $\tau$?