0
votes
0answers
10 views

Probabilistic Graphical Model Diagram Notation, what does the box mean?

I'm just learning about probabilistic graphical models, I know the circles represent random variables, shaded being observed and unshaded being latent variables. But what does the box mean?!
2
votes
0answers
37 views

What does the notation $\textbf{x} \langle\textbf{Y} \rangle $ mean if $\textbf{Y} \subseteq \textbf{X}$ for random variables?

I was reading daphne's Probabilistic Graphical Models book and she introduces some notation about sets of random variables that I am confused about (on page 21 section 2.1.3.2). Before I ask my ...
0
votes
2answers
47 views

Probability notation P versus Pr

I have come across both $P(…)$ and $Pr(…)$ being used to represent probabilities. Is there any difference in the meaning of these notations, or are they just different shorthands? I seem to come by ...
0
votes
1answer
34 views

What are the different ways of indicating that a random variable has a specific distribution?

Recently I have seen random variable distributions described in two ways: $$ X \sim Nb(r,p) \\ X \stackrel{d}{=} Nb(r,p) $$ Both indicating that $X$ is a negative binomial random variable with $r$ ...
2
votes
1answer
114 views

“unity symbol” from Feller's “An Introduction to Probability”

I am wondering if anyone knows the name or source of the symbol shown below from page 22 of the Second Edition of Feller's "An Introduction to Probability" Volume I.
0
votes
2answers
28 views

How do you write the set where $2$ numbers are chosen

A = the event that the sum of outcomes of $2$ dice being thrown So do I say $A = \{14;41;23;32\}$ That looks like I'm saying $41$ (the number) not $4$ from one die and $1$ from the other which ...
0
votes
1answer
41 views

subscript notation in conditional probability

$X$ and $Y$ are two discrete random variables with joint p.m.f $p_{XY}$ such that $p_{XY}(x_i,y_j) = P(X=x_i, Y=y_i)$. I came across a notation that refers to $p_{X}(x|y)$. How do I express it in the ...
1
vote
2answers
81 views

What does $\vee$ mean in set theory?

The following proof is from Probability by Davar Khoshnevisan. There is a symbol $\vee$ in the third sentence of the proof. What does this symbol mean, please? There seems no definition about it in ...
1
vote
1answer
29 views

What is the meaning of this notation?

I am watching this video on maximum likelyhood estimation. I'm confused by the notation when the presenter says "assume a set of distributions P-theta." (the URL links to the relevant part of the ...
3
votes
2answers
88 views

In probability notation: what does a tilde over a letter mean?

I am reading this paper. In section 1.1 he says: What do the tildes above the letters mean? How can I translate these two sentences into ordinary English?
1
vote
1answer
28 views

Understanding $Po(np)\{A\}$ probability notation

I am trying to read a textbook on probability and am already stuck on what must be basic notation. It says Thus, for example, if $A$ is any subset of $\mathbb{Z}^+$, it follows that for some ...
1
vote
2answers
166 views

What does P(A U B) mean, in terms of real values?

I can't find a proper summary or reference of how to translate formulas in probability notation to arithmetic notation (i.e. when using real values). For example, if $P(A) = .7$ and $P(B)=.35$, what ...
0
votes
1answer
73 views

Is there a symbol for “dependent”?

For random variables $A$ and $B$, $A \perp B$ is sometimes used to denote "A in independent of B". Is there a symbol that is commonly used to mean "A is not independent of B"?
0
votes
1answer
25 views

How to describe a set of coordinates of variable length?

I need to describe a set of coordinates with up to 8 dimensions. A problem is asking me to describe an event from a experiment involving sampling. The catch is that the experiment doesn't end until a ...
0
votes
1answer
54 views

Confused with probabilistic notation and precedence

Is $P(A|B,C) = P(A|(B \cap C))$ or $P((A|B) \cap C)$? In my book they do something like this in a proof regarding Markov models: $P(A|B_{1:t+1}) = P(A|B_{1:t},B_{t+1}) = ...
0
votes
2answers
184 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 ...
0
votes
1answer
47 views

Name and notation convention for “unnormalized probability”

Given a finite set of non-negative numbers $S={s_1,...,s_n}$, we can divide them by a normalization constant $Z$ (i.e. their sum) to get a probability distribution. Then we typically say (and write) ...
0
votes
2answers
79 views

Probability notation?

I've tried to gather information about these three topics i'm about to show but i couldn't find. I will display them in a question for better understanding and context of the situation. For a ...
3
votes
1answer
126 views

What does the notation $P[X\in dx]$ mean?

I am studying probability, specifically regular conditional distributions, and came across the notation $P[X\in dx]$. What does this mean? Here, $X$ is a random variable and $P$ is a probability ...
1
vote
1answer
67 views

Symbol for “is closest to”?

I am writing a paper on probabilities and we have to find a $k$ such that $P_n(k)$ is "closest to" $P_0$. $P_0$ is getting 4-of-a-kind in a five card hand in a standard 52 card deck. $P_n(k)$ is ...
0
votes
1answer
82 views

What does this notation mean? $f(x|\theta)=\frac{3x^2}{\theta^3}I_{(0,\theta)(x)}$

Particularly I want to know what the meaning of $I_{(0,\theta)(x)}$ is here.
0
votes
1answer
98 views

What is the dot product between a vector of matrices?

There is a notation used in many sources (e.g. Wikipedia: http://en.wikipedia.org/wiki/Exponential_family) for the natural parameters of exponential family distributions which I do not understand, and ...
0
votes
1answer
71 views

Notation confusion in the Wikipedia article on the Law of Large Numbers

In my infamous attempt at mastering (at my humble level) the "art" of probability and statistical theory, I was reading the Wikipedia article on the Law of Large Number and got confused by a couple of ...
3
votes
2answers
1k views

What does the Big intersection or union sign of a set means?

Normally what I know is that you can make a union or an intersection between 2 sets. In this expression Its a big union of a set. I'm asking about the meaning of such expression, What does it mean. ...
1
vote
1answer
57 views

What is the notation for separable states or independent variables?

Is there any specific notation that two quantum states are separable or that two random variables are independent?
2
votes
2answers
107 views

Understanding notation difference between mutual information and information divergance

The mutual information is defined on random variables. That is, $I(X;Y)$ denotes the mutual information between random variables $X$ and $Y$. On the other hand, the the Kullback-Leibler divergence is ...
0
votes
3answers
144 views

What is the answer to $(1/10000000)^{455}$ in scientific notation?

I'm trying to figure out the odds of a random generator generating the same list of numbers $455$ times in a row. The random numbers are in a range from $0-1.999999$ ($6$ decimal points) I figure ...
1
vote
1answer
153 views

What does $P(\overline{N})$ mean?

Sorry, this must be laughably trivial, but I have to be sure. I am a grade 12 math tutor, and while running through some older exam questions I encountered this problem: $$\text{If } P\left(N\right) ...
2
votes
1answer
51 views

Help with ambiguous notation

I am reading Probabilistic and Graphical Models, and uncertain about the meaning of the following use of the notation $\mathbf{I}$. The textbook defines the use of $\mathbf{I}$ to mean flow of ...
2
votes
3answers
1k views

Notation of random variables

I am really confused about capitalization of variable names in statistics. When should a random variable be presented by uppercase letter, and when lower case? For a probability $P(X \leq x)$, what ...
0
votes
1answer
241 views

Symbol for Mutual Inclusive events

is there any symbol for mutual inclusive(opposite of Mutually exclusive) events in probability. I meant to say is for OR we have U symbol in Set Theory. Likewise ...
1
vote
0answers
161 views

How to denote a random variable and the set of possible values

I'm curious what the most common way is to denote a random variable and the set of possible values that it can take on. I doesn't seem correct to say, for instance: $r.v.\ X \in \{\ldots\}$, because ...
1
vote
2answers
89 views

What exactly does this physically mean?

Let X(w) be a real random variable on ($\Omega$ , P). The image X($\Omega$) the set of all the values X(w) can take ,written $\Omega^{X}$. For any set $ B \subset \Omega^{X}$ the probability of the ...
2
votes
1answer
85 views

Mathematical Symbol

In the following paper, what does the symbol $\Phi$ in equation $3.1$ (page $3$) represent? Does it represent the normal distribution?
2
votes
2answers
278 views

Probability notation

Hey guys, I was just wondering why in my textbook(A First Course in Probability, 8th edition) and basically everywhere I've looked at when we have some random variable(assume for the sake of the ...
2
votes
1answer
526 views

What is the difference between a probability distribution on events and random variables?

For the purpose of simplicity, assume everything below is only in the discrete domain. A $\text{probability space}$ is usually defined as a triple $(\Omega , 2^\Omega , P)$ where $\Omega := ...
3
votes
1answer
37 views

Is it necessary to state that $y_i \leq 1$

In a class test for Linear Programming, my professor deducted some marks because I missed the condition $y_i \leq 1$ in the mixed strategy games solution. $ y_i $ stands for the probability of any ...
4
votes
3answers
97 views

Notation for $X - \mathbb{E}(X)$?

Let $X$ be a random variable with expectation value $\mathbb{E}(X)=\mu$. Is there a (reasonably standard) notation to denote the "centered" random variable $X - \mu$? And, while I'm at it, if $X_i$ ...
0
votes
1answer
48 views

Expression Writing: Random variable inside bayesian (Notation)

What is the best, most clear way to denote this example. Event A: outcomes (0,1). P(C)=P(B), if A=1 P(C) = 0, if A=0 Which one is best 1) P(C) = P(B|A=1), A: indicator random variable 2) P(C) ...
2
votes
0answers
210 views

Writing a probability expression (Notation)

What is the best way to denote, Probability of $n_i$ changing its value from $0$ to $1$ at time $t$. I come up with these, any suggestions _ $$ P_{n_i,0\rightarrow1}(t) \\ P(n_i:0\rightarrow1, t) $$ ...
0
votes
2answers
91 views

Notation for probability of either sign

I have a function $f(k) = \pm 2^k$ with probability $1/2$ of either sign. How would I express this in a cleaner notation? I'm guessing to use the Kronecker delta somehow, but I can't put a finger on ...
6
votes
1answer
74 views

what does $\alpha(N)$ mean in this article?

I'm trying to understand this article: http://imgur.com/a/HfJoY but I'm unsure what $\alpha(N)$ means in this context? Is it the algebraic multiplicity, that's pretty much the only $\alpha$ I have ...
7
votes
2answers
1k views

Notation for probability density

On one of my other questions here, I was criticized (and rightly so, as it was the source of my mistake) for using this notation for a continuous random variable $X$ with pdf $f(x)$: ...
1
vote
0answers
51 views

What does $\Delta P_{t+1}(n)$ mean?

In Physics, there is a chapter about "Statistical Mechanics" where I do not really understand a notation: Let there be four coins, each of which can be either heads or tails. Set them in a given ...
-4
votes
3answers
144 views

What is the meaning of $P(A \cup B)$ in probability and statistics?

In probability, letters $A$ and $B$ are used to denote various events. Then we write $P(A)$ for the probability of event $A$ happening. Same for $P(B)$. But I often see the notation $P(A\cup B)$ as ...
2
votes
1answer
217 views

How a random variable takes a value?

Why do mathematicians say a random variable takes on a value? Is it just for convenience? My understanding is that a random variable is a function mapping the sample space of an experiment to a ...
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 ...
1
vote
1answer
67 views

How is $I_{[0,\infty)}(t)$ defined?

How is $I_{[0,\infty)}(t)$ defined? This must be a notation in probabilty theory.
2
votes
1answer
254 views

Notationally, what is the difference between $\Pr(X = x)$ and $P(X = x)$? When should I use each?

I'm talking specifically about probability theory. I was reading some stuff about probabilistic graphical models, and they kept switching the notation in this book, but I couldn't discern the ...
2
votes
2answers
396 views

Set operators vs. Logical operators while discussing probability theory.

Let $S = \{1, 2, \dots, 10\}$ Let $A$ be the event that a number selected from $S$ is even. Let $B$ be the event that a number selected from $S$ is a multiple of $3$. If any number is equally likely ...