1
vote
2answers
269 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.
1
vote
2answers
46 views

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 ...
1
vote
0answers
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 ...
0
votes
1answer
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 ...
1
vote
2answers
34 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 ...
3
votes
1answer
70 views

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 ...
2
votes
3answers
61 views

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 ...
0
votes
0answers
10 views

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 ...
1
vote
0answers
22 views

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, ...
0
votes
2answers
50 views

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 ...
0
votes
2answers
195 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 ...
2
votes
2answers
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 ...
0
votes
1answer
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 ...
1
vote
4answers
97 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 ...
0
votes
2answers
70 views

What is a two point support in this lemma?

What is the terminology of two point support in this lemma?
1
vote
4answers
131 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 ...
2
votes
1answer
38 views

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 ...
1
vote
1answer
67 views

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 ...
1
vote
1answer
114 views

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? ...
2
votes
2answers
178 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 ...
0
votes
1answer
128 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 ...
2
votes
2answers
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 ...
3
votes
0answers
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 $S(x,y):=\sup_n p^n(x,y)$. ...
3
votes
1answer
482 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 $h \in H$ ...
4
votes
1answer
252 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 ...
2
votes
1answer
77 views

Looking for the Name of this property: $\mathsf{P}\left(X \leqslant x\right) = \mathsf{P}\left(h(X) \leqslant h(x)\right)$

$h(\cdot)$ denotes a strict monotonic increasing transformation such as $\log$. Another inequality I do not quite get is that $$\mathsf{P}\left(h(X) \le h(x)\right) \ge \mathsf{P}\left(X \le ...
1
vote
1answer
90 views

Am I talking right?

I'm trying to describe expected value. My paragraph goes: From probability theory we have $E[f(x)] = \int{f(x)p(x)dx}$. That is, the expected value of $f(x)$ is equal to the sum of infinitesimals ...
0
votes
1answer
131 views

Meaning of the term single letter formula

It is common in information theory to look for single letter formulas or to dismiss a result as suboptimal if no single letter formulas are available. Could someone clarify the meaning of what is a ...
0
votes
1answer
186 views

Name of probability distribution

Does this distribution have a name: $f(x) = yx^{y-1}$ for $0 < x<1$ and $y>0$? It looks like an exponential distribution. Or is it a nameless distribution?
3
votes
3answers
185 views

Probability Term for something that defies the odds.

I'm not a mathematician; I just wandered over here from Writers SE and am hoping you guys can help. I'm writing a novel in which the theme is characters beating the odds. (It's a future dystopia, the ...
1
vote
1answer
261 views

Turning a Product of Events into a Product of Conditional Probabilities

Is there a name for the following identity? $$ \begin{align*} & \Pr\left(\bigwedge_{i=1}^n A_i \mid B \right)\\ &= \Pr\left(A_1 \mid B \right) \cdot \Pr(A_2 \mid A_1 \wedge B) \cdot \Pr(A_3 ...
1
vote
2answers
172 views

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 ...
5
votes
1answer
153 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 ...
2
votes
2answers
928 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 ...
2
votes
2answers
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 $\tau$?
18
votes
3answers
17k views

Probability density function vs. probability mass function

I've an confession to make. I've been using pdf's and pmf's without actually knowing what they are. The idea that I've been having so long is that density = area under the curve but if I look at it ...
1
vote
2answers
118 views

Terminology for handling probabilities with partial knowledge

Consider a situation where a person has partial knowledge, but we have a more complete picture. For example, suppose that we want to know the probability that a fish is red. Suppose that the person ...