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# Questions tagged [probability]

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

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### Expected value of min X for bernoulli success?

I take a SRS sample of size n from a population of x values ranging from 1 to N. Each selected unit also has a probability p of success or q = 1-p of failure (i.e. the probability of success/failure ...
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### What is the Johnson family of distributions good for? What are their main features and applications?

I saw the Johnson family of distributions in context of reliability and demand modeling for supply chains, but I am not sure if they are bringing real benefit to pay for their relatively more complex ...
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### Understanding proof of McDiarmid's inequality

I am working through Wasserman's lecture notes set 2 and I am unable to fill in the missing steps in the derivation of McDiarmid's inequality (p.5). Just like my previous question in the forum, I am ...
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### Error count limit for known residual failure rate and desired false-positive rate?

We perform a known fixed number $K$ of independent experiments, each of which has known/assumed residual odds $p$ to fail. We count the number $N$ of failures. How can I choose $M$ so that $N>M$ ...
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### What is the probability that two independent random vectors with a given euclidean distance $r$ fall in the same orthant?

Consider two independent and identically distributed random vectors of dimensionality $N$, $\mathbf{x}$ and $\mathbf{y}$, where their elements are iid generated from a Gaussian with zero mean and ...
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### probability of the next number of events occurring when the true probability is known [duplicate]

Possible Duplicate: Probability of getting between What is the probability that at least 24 of the next 50 people like to swim when the true probability of people liking to swim is 35%? I ...
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### Taking random items out of a container with replacement

I take vitamins in the morning, but one of them I only take a half tablet. So, I have an initial container with 100 full tablets, and every morning I take out a random tablet. If it's a full ...
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### Finding a minimum variance unbiased (linear) estimator

Here is a basic question that perhaps has a simple answer, but one that I was not able to find by quickly scanning the literature. Suppose that I have a collection of $n$ unopened boxes. Each box $i$...
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### Does an exact test always yield a higher P value then an approximated test?

I ran a simulation on that for mcnemar test, and the answer seemed to be yes. I was wondering if this can always be said to be the case that the exact P value is higher (or not smaller) then the p ...
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### Learning probability and statistics together

I posted a question earlier where I mentioned that I am interested in learning Machine Learning but that my background in statistics and probability is pretty weak. Recently I previewed pages of 2 ...
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### Odds that the jack of trump dealt 46% of time in pitch

In the game of Pitch what are the odds of the jack of trump being dealt in the 24 cards?
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### Likelihood of errors based on a sample

I frequently do something like: load a bunch of data, and then scan some fraction of it randomly to verify that no errors occurred. The more data I verify, the greater my certainty that no errors ...
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### Finding top n across multiple sets

Suppose we have a set of key value pairs, such that the keys can be ordered based on the value . We can easily extract and report the top $n$ keys. Now suppose the we havet S such sets. From each set ...
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### Expected number of unseen cards when drawing $2n$ cards from a deck of size $n$

We have a deck of $n$ cards. We draw cards from it uniformly at random with replacement. After $2n$ draws what is the expected number of cards never chosen? This question is part 2 of problem 2.12 in ...
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### What is the P(A|C) if we know B depends on A and C depends on B?

Given a Bayesian network that looks like the following: A->B->C How do we compute P(A|C)? My initial guess would be: ...
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### What is the intuition behind the score function? [duplicate]

Wikipedia tells us that the score plays an important role in the Cramér–Rao inequality. It also phrases out the definition: $$V = \frac{\partial}{\partial \theta} \log{L(\theta; X)}$$ However, I ...
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### Dice probability for Yahtzee large straight

I had a discussion with a friend of mine about what is the best course of action in the following Yahtzee scenario: The first throw with 5 dice results in the following values: ...
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### What is a normal distribution with 'common variance'?

Data Augmentation Approach in Bayesian Modelling of Presence-only Data (Divino et al.) states that the data ware sampled from a normal distribution with mean 2.0 and a common variance (section 3). ...
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### Learning to create samples from an unknown distribution

I am interested in new generating samples to approximate some unknown distribution X, where each new sample is a real-valued vector. The purpose it to be able to create a new (arbitrary large) ...
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### If the n(th) moment exists does it mean all smaller moments exist too?

I would like to prove the following statement: If the $r$th moment of a random variable $X$ exists and is finite, then all moments $1$ to $r-1$ exist and are finite. Edit: I mean the raw moments ...
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### Tuning the birthday paradox [closed]

There are m disjoint sets Xi and a function f : [1..n] → [1..m] such that Yj = Xf(j). I am given oracles / samples from random variables xi and yj which uniformly select elements from Xi and Yj ...
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### How can the F distribution be used, other than for hypothesis testing and confidence interval estimation?

I am trying to fit informed prior distributions to data using MLE, and F occasionally provides a best fit (lowest AIC value). I am starting with only very basic knowledge of probability theory, so I ...
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I need to study in depth the on/off problem with different approaches: frequentist, bayesian - frequentist hybrid, profile likelihood. The on/off problem is a counting experiment where you observe $... 5 votes 1 answer 7k views ### Expectation of length of a confidence interval Let$X_1,X_2,X_3,\cdots,X_9$be a random sample of size$9$from a normal distribution,$\mathcal{N}(\mu,\sigma^2)$. If$\sigma$is unknown, find the expected value of the length of a$95\%$... • 159 1 vote 1 answer 1k views ### How to compute mean vector and covariance matrix of equal distributions? This question is an extended version of this one. As you can see here, two distributions are equal, I need to compute the parameters a,b,c,d and e. Could you show me a way to do that? Assume a two-... 1 vote 1 answer 1k views ### What does "equal a priori class probabilities" mean? I am trying to solve a problem about my homework. The problem says that Assume a two-class problem with equal a priori class probabilities Does it mean, mean vectors and covariance matrices ... 3 votes 1 answer 247 views ### Plain English explanation of Bernoulli mixture models? Not exactly the most accessible explanation can be found here, but I'm looking for something more intuitive, examples of applications and so on. Help is much appreciated. • 7,011 9 votes 3 answers 781 views ### What does Jaynes' continuous pdf notation "$g(x)~\mathrm dx\$" actually mean?

Something has been bugging me about E.T. Jaynes' treatment of continuous parameters. In his book Probability Theory: The Logic of Science, uses notation that I am unfamiliar with when getting ...
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