Questions tagged [probability]

A probability provides a quantitative description of the likely occurrence of a particular event.

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2
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1answer
63 views

Probability of A given B and C

I'm trying to write an algorithm and I'm rusty on my statistics. Basically my question comes down to how do you get the probability of A given B and C. I'm trying to walk myself through a made up ...
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1answer
65 views

Expected min distance between N Uniform RVs

Inspired by this recent question, what is the expected value of the minimum of the pairwise distances between $N$ uniform and independent RVs (uniform in $[0,1]$)? i.e. Let $X_1,...,X_N$ these RVs, ...
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1answer
35 views

Conditional Probability Question in a Diagram

I know Pr(X2 = T | X3 = F) = Pr(X2 = T, X3 = F) / Pr(X3 = F) but I don't know how to figure out each probability individually. Anyone have any idea how to do it?
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Why this could not be represented by a Bayesian network

A, B, C, D are four variables. Why $A \perp C | \{ B , D \}$ and $B \perp D | \{ A , C \}$ could not be represented by a Bayesian network?
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Solving argmin $E[(Y-c)^2 | X]$ [duplicate]

While reading a book on statistics, I encountered the following: $$f(x) = \mathop{\text{argmin}}\limits_c E_{Y|X}([Y-c^2]|X=x)\tag{1}$$ which somehow equates to $$f(x) = E(Y|X=x)\tag{2}$$ How do we ...
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1answer
31 views

Conditional Probability Question from Diagram [closed]

Anyone have any idea how to approach this problem?
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1answer
26 views

Symbol of precision and precision matrix

This is one of my first questions so sorry in advance for any rules that I break. Is there any mainstream convention for the symbol of the precision and precision matrix? I have seen the following ...
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27 views

Estimate population variance / mean from truncated distribution with known cutoff, but without parametric assumptions

Suppose you have a sample of $N$ iid random variables $X_i$ drawn from an unknown (but finite variance) distribution but with a known upper-cutoff $K$ and therefore support $[0,1,2,...,K]$ but un-...
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Rewrite joint probability as product of marginals when all the probabilities are $1$ or $0$

I have a question about the possibility of rewriting a joint probability as the product of the marginals when all the probabilities can only take value $1$ or $0$. I start with introducing some ...
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0answers
18 views

Probability of two coins having the same bias

Assume that we have two coins and also assume that probability of heads for coin A is x and probability of heads for coin B is y. Given the below two random and independent trails: ...
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1answer
28 views

Random matrix theory and research - a lot like doing linear algebra?

I've been searching for a subfield of research to get into and wonder whether random matrix theory could suit me well; it seems like it does, because the stuff I read, and the seminars that I watch ...
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1answer
42 views

Does this probability make sense: p(x)p(x|a)? [closed]

Let's say x is some event occurring, $p(x)$ is the probability of x occurring, and $p(x|a)$ is the probability of event x occurring given event a has occured. Does this probability make any sense, and ...
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1answer
122 views

How to calculate the posterior probability with bayesian theory?

The Bayesian formula is given as the following simple way. $${\mathsf P}(a\mid x) ~=~ \dfrac{{\mathsf P}(x\mid a)~{\mathsf P}(a)}{{\mathsf P}(x)}$$ A factory makes pencils. prior probability: ...
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1answer
45 views

Find probability using Z-scores - don't understand solution

Graduate students applying for entrance to many universities must take a Miller Analogies Test. It is known that the test scores have a mean of 75 and a variance of 16. In 1990, 50 students applied ...
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57 views

Convolution of a multivariate Gaussian and multivariate exponential distribution

I have derived the convolution for a multivariate Gaussian distribution with a multivariate exponential distribution. The aim is to get a multivariate extension to the univariate exponentially-...
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30 views

Product of normal random variables and exponential random variables is exponential random variables?

How we can prove analytically, the Product of normal random variables and exponential random variables is exponential random variables?
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1answer
55 views

Interpretation of the technical requirement on a random variable

I found a slide where there is the definition of a random variable and after a technical requirement difficult to understand for me. Can you explain it by using a counterexample please? What happens ...
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1answer
38 views

Develop intuition for conditional probability composition

I have heard many sources state that this is inherently non-intuitive, however maybe somebody here has broken the code and can help. Scenario described based on video. In the scenario we have two ...
2
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1answer
21 views

Mixed order and unordered counting

If you care about ordered or unordered counts you can use nCr or nPr. But If you want a few in a certain order and a few unordered is there a general approach? For example imagine you have 6 red ...
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1answer
69 views

Unique game problem (ML, DP, PP etc) [closed]

Looking for a solution to my below game problem. I believe it to be some sort of dynamic programming, machine learning, or probabilistic programming challenge, but am unsure... This is my original ...
2
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1answer
21 views

Rationale behind Q-learning

I am reading Sutton Barto on Reinforcement Learning. I understand that $TD(\lambda)$ methods propose better performance than Monte Carlo methods, with TD methods combining advantages of Dynamic ...
2
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1answer
37 views

Is this series divergent?

I have $$G_N = \sum_{i=1}^{N} \left\{ \frac{1-\pi_i}{\pi_i} + \frac{1-\pi_i}{T\pi^2_i}\right\} (y_i-\theta)^2=\sum_{i=1}^{N} V_i$$ where $2\le T\le 10$, $0\le \pi_i\le1$ and suppose $y_i\sim N(\theta,...
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Model to Bootstrap/ simulate hourly shape from daily data

How do I simulate/boot strap hourly shape from daily data ? $\mathbf {Data set:}$ My first data has hourly granularity, its hourly temperature, $T_1$ through $T_{24}$ and but I have no means to ...
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1answer
51 views

Is this statement true, and how can I prove it? [closed]

Suppose we got a tree of probablities, of non independent probablities like this: Path-1 : 0.5*0.7*0.8*0.9 = 0.252 Path-2 : 0.5*0.8*0.8*0.9 = 0.288 Path-3 : 0.6*0.9*0.7 = 0.378 suppose the ...
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23 views

Questions Regarding Conditional Entropy

I have a question related to a conditional entropy that I have to solve and I struggle a bit on the understanding of my implementation. So I formalized the questions here as follows. Any suggestions ...
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1answer
37 views

Rolling d20, d12, d10, d8, d6 in a row, what's the probability of a 1 on at least one of the rolls?

So I roll a d20, d12, d10, d8, d6, one at a time, in a row. What are the chances of at least one roll to be a 1? And how do you calculate it?
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1answer
20 views

Intuition behind difference between specific sequences and sequences with specific properties?

I simply cannot wrap my head around this fact: "A fair coin is no more likely to produce any specific 10-toss sequence than any specific other one, but it is about 250 times as likely to produce one ...
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1answer
41 views

Can anyone help to explain one of the variables in a figure that illustrates how posterior probabilities shift and move around?

I am learning this post. The book gives this figure to illustrate how posterior probabilities shift and move around Here is the code ...
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1answer
17 views

Notation in definition of a quantity involving uncertainty and posterior probability

As a probs & stats noob, I'm still getting confused by notation. I would appreciate if someone could elaborate a bit on what's going on here, on p12 of Settles' Active Learning survey (2012). He ...
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2answers
166 views

Why is the total probability theorem expressed in this way?

The total probability theorem states the following: Let $A_1$,...,$A_n$ be a partition of $\Omega$. For any event B, $$Pr(B)=\sum_{i=1}^n Pr(A_i)Pr(B|A_i)$$ We know that $Pr(B|A_i)= \frac{Pr(B\cap ...
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1answer
17 views

Temporal difference definition (Reinforcement Learning)

Reading for instance Szepesvari or this : i struggle to understand the rationale behind the temporal-difference definition $\delta_{t}=R_{t}+\gamma V_{k}(x_{t+1})-V_{k}(x_{t})$ with the notation ...
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1answer
21 views

Measure like relative frequency that also weights the total [closed]

Background I see a lot of publications mentioning relative frequencies to indicate the presence of certain genes in a specific area. For example: ...
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1answer
47 views

Expected value of $e^{vS}$, where $S$ is an exponential

I am studying queueing theory and in particular I am dealing with priority queues with preemption. I found this very interesting paper that treats various topics of interest. The system is composed ...
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1answer
26 views

Conditional probability for binary events [closed]

I have 2 columns of data called level 1 event and level 2 event. Both are columns of 1s and zeros. I want to find the probability of a level 2 event given that the previous event was a level 1 event....
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99 views

Is there a standard name for this continuous distribution? [closed]

I'm encountering the following PDF of continuous scalar real $X$ with semi-infinite support $]0,+\infty[$: $$ f_X(x) = C ~ x^{-\alpha} ~_1F_1\left ( a,b;-\frac{d}{x^\beta} \right ),~~~~~~\beta>0;~\...
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1answer
37 views

Poisson-gamma posterior mean expectation

Let's have a gamma prior $\lambda\sim \operatorname{Gamma}(a,b)$ (mean: $\frac{a}{b}$) With Poisson data $Y\mid \lambda\sim \operatorname{Pois}(N\lambda)$ (mean: $N\lambda$) The posterior is $\...
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0answers
29 views

Maximum Mean Discrepancy Implementation

I am just beginning to learn about MMD as a way to measure the difference between two probability distributions using this tutorial. I want to implement it code-wise but I don't understand it ...
2
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1answer
45 views

Waiting time distribution parameters given expected mean

I have a set of healthcare providers serving patients. In a given amount of time, a specific provider can see only a certain amount of patients, depending on the medical procedure and other variables. ...
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1answer
21 views

Is it possible to calculate the scale param θ for the Gamma distribution, given shape param K and a quantile value Q?

Stats-ophils, I am running into a problem, in which I'd like to generate a Gamma distribution (in Julia) and I know the value of the quantile Q(0.9) = 130 as well as the shape parameter k=2. Is it ...
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37 views

probability/counting problem

This is an even question from the textbook so unfortunately there's no solution. Suppose $\DeclareMathOperator{\P}{\mathbb{P}} S = \{1,2,3,4,5,6,7,8\}$ with $\P({s}) = 1/8$. Part C) asks How many ...
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1answer
48 views

Why must probability fields be closed under countable unions?

Assume a probability triplet $(\Omega, \mathcal{F}, \mathbb{P})$. My current understanding of $\mathcal{F}$ is that it must define events i.e. the subsets of $\Omega$ where probability is defined. I ...
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2answers
92 views

Sum of a random number of r.v.'s [closed]

A fair coin is flipped independently until the first Heads is observed. Let the random variable K be the number of tosses until the first Heads is observed plus 1. For example, if we see TTTHTH, ...
2
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1answer
54 views

Simulating a queue in R [closed]

It's noted that the number of folks in a stationary system will maintain an average equal to the rate of arrival multiplied by the mean of the service distribution. Where the formula $L = \lambda$ ...
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1answer
37 views

Probability of 100,000 Computer parts, if one computer part lasts more than seven years is $0.4966$

If the length of time the computer part lasts is exponentially distributed with mean value is $10$. So, for the exponential distribution, we can find the probability of one computer parts. $$p(x>...
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1answer
23 views

Confidence Intervals when Assigning Inidivdual (Non-numerical) Data Points in a Sample To One of Four Categories

I'm breaking down email addresses into four categories. I'd like to know what probability distribution model I could use to calculate confidence intervals that the ratio of addresses fitting into each ...
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0answers
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Cox regression: Estimate the value of covariate which gives a survival probability of 50 % at a specific time point

I have a data set of 150 individuals where 30 experience the event, all at different time points. I've fitted a cox regression model using step-wise backward selection and the model came out with one ...
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0answers
22 views

Extract data from mainly unstructured sets and derive risk metrics out of those

I have the following question (this was a real life problem): Q: Extract data from mainly unstructured sets and derive risk metrics out of those. From what you know or imagine about the data ...
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0answers
56 views

Does this statistical distance have a name and does the triangle inequality hold?

Let $P$ and $Q$ be two distributions on $\{1,2,\dots,n\}$. Define their distance by $$d(P, Q)=\Pr_{X\sim P,Y\sim Q}[P(X)Q(Y)>P(Y)Q(X)]\,,$$ where $X$ and $Y$ are independent. I could show that $d(...
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1answer
30 views

Calculations in a Bayes Network

I am working through a text book (Probabilistic Graphical Models, Principles and Techniques) to learn BNs, but I am confused as to the accuracy of the example. The text references the figure above. We ...
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1answer
17 views

Non-Linear probability scale (y-axis)

Very new to stats so excuse me if my terminology is wrong. Hi, trying to plot a log probability plot and don't know the equation to use to generate the y axis. With 50% mean I am trying to achieve ...