# Questions tagged [probability]

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

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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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### 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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### 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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### Conditional Probability Question from Diagram [closed]

Anyone have any idea how to approach this problem?
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### 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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### 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 ...
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: ...
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 ...
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 ...
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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### 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 ...
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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### 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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### 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 ...
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 ...
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 ...
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 ...
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 ...
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### 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 ...
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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### 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 ...
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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### 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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### 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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### 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 ...
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(...