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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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### What model is most appropriate to estimate the probability of something occurring? [closed]

e.g. estimate the probability that of 10 (ten) small businesses 3 (three) or less will fail in the first year of operation
104 views

### Determining the significance of a set ordering [closed]

First some preamble: Let A be a set of unordered elements, and let A' and A'' be subsets of A, where |A'| = |A''| = k. It’s given that as k approaches |A|, for every x in A' there is an increased ...
1 vote
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### Expected value of a random variable in a range

I have a random variable $x$ with $E(x) = \mu$ and PDF $f(x)$ and CDF of $F(x)$. Is there any way to represent the $E(x|x<\bar{x})$ in terms of $\mu$ and $f(x)$ or $F(x)$? i.e. to write the ...
5k views

### Meaning of p-values in regression

When I perform a linear regression in some software packages (for example Mathematica), I get p-values associated with the individual parameters in the model. For, instance the results of a linear ...
1k views

### Combining two pieces of evidence expressed as probabilities

I have a hidden binary random variable Z that can have a value of either 1 or 0. There is some true probability P(Z=1) = z that I do not know. I also have two separate pieces of "evidence" that give ...
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### Fitting a probability distribution to zero inflated data in R

I am trying to learn how to fit a probability distribution to a vector of data, using the program R, but there are a lot of potential probability distributions to use! So my question is, how do I ...
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### How can I estimate the probability of a random member from one population being "better" than a random member from a different population?

Suppose I have samplings from two distinct populations. If I measure how long it takes each member to do a task, I can easily estimate the mean and variance of each population. If I now hypothesise ...
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### Random walks in multinomial case

Model: A vector $X=(X_1, X_2, X_3)$ that follows a trinomial distribution with parameters $p=1/3$ and $n$. (I have a coin with three sides $S1$, $S2$, $S3$). I flip the coin $n$ times. The coin has ...
4k views

### How to compare proportions across different groups with varying population sizes?

I am trying to understand what statistical measures I can use to compare three groups having varying populations to understand which group is bad (highest probability of death or most vulnerable or ...
4k views

### Designing a test for a psychic who says he can influence dice rolls

Let's say that I have a friend (let's call him "George") who says that he can control the roll of dice using his mind (ie, make the dice more likely to fall on a specific number he is thinking of). ...
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### How to compute the Kullback-Leibler divergence when the PMF contains 0s?

I have the following timeseries obtained using the data posted below. For a sliding window size of 10, I am trying to compute the KL-divergence between the PMF of values within the current sliding ...
1k views

### What is the $i$th sufficient statistic in the EM algorithm for Gaussian mixture models?

I am reading up on the EM algorithm for Gaussian Mixture Models, and there is consistent reference to the $i$th sufficient statistic. What is this, and why is it relevant to the algorithm?
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### What is the best way to learn the fundamentals of probability required for machine learning algorithms?

I took a probability course in university a few years ago, but I'm going through some machine learning algorithms now and some of the math is just befuddling. Specifically right now, I'm learning ...
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### Probability of an event that is not measureable

We know from measure theory that there are events that cannot be measured, ie they are not Lebesgue measureable. What do we call an event with a probability that the probability measure is not ...
184 views

### How to visualize iterative parameter constraint?

I have conducted an analysis in which I start with a set of informed prior parameter distributions, and then conduct sequential analyses that constrain the distributions with data. I am currently ...
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### How to compute the probability associated with absurdly large Z-scores?

Software packages for network motif detection can return enormously high Z-scores (the highest I've seen is 600,000+, but Z-scores of more than 100 are quite common). I plan to show that these Z-...
204 views

### Generalization of basic probability question

This is the motivation for my question: Suppose we have $n$ tickets in a bag, and we draw $k$ of them uniformly at random without replacement. Now, repeat the same procedure independently (same $n$ ...
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### How can I calculate a probability from a likelihood, e.g. in the Metropolis-Hastings algorithm?

This is a follow-up to my previous question, how can I compute a posterior density estimate from a prior and a likelihood I am having difficulty understanding how it is possible to calculate the ...
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### Probability of drawing no red balls from 20 draws without replacement given finite sample

I understand this to be a binomial distribution: There are 100 balls in a bucket. 10 are red, 90 are blue. I select a ball at random and then replace it in the bucket, and I do this 20 times. I then ...
370 views

### Probability of total events occurring given that one or more events occur in specified number of months

As a non-statistician, I have a real world statistical/probability problem that I'm having trouble framing. The software I rely on in inventory management interprets the 'movements' (number of times ...
5k views

### How to define a distribution such that draws from it correlate with a draw from another pre-specified distribution?

How do I define the distribution of a random variable $Y$ such that a draw from $Y$ has correlation $\rho$ with $x_1$, where $x_1$ is a single draw from a distribution with cumulative distribution ...
367 views

### Distributing values according to a given continuous probability distribution

I have a series of continuous probability distributions and the intervals for each distribution of possible values. Now I want to use the distributions to distribute values of a random variable among ...
4k views

### How to turn a function into a probability density whilst maintaining the shape of the function?

I have a series of functions, each one supposedly representing the density of a random variable across agents. Each function also has a domain, which describes what values of the random variable are ...
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### How to compute co-occurrence probability assuming independence from unigram probabilities?

I have a text corpus, from which I have computed the unigram probabilities of every word. Now, let $p_{i}$ & $p_{j}$ be the unigram probabilities of $i$ and $j$ respectively, what will be the ...
899 views

### What is the distribution of maximum of a pair of iid draws, where the minimum is an order statistic of other minima?

Consider $n\cdot m$ independent draws from cdf $F(x)$, which is defined over 0-1, where $n$ and $m$ are integers. Arbitrarily group the draws into $n$ groups with m values in each group. Look at the ...
1 vote
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### Building business intelligence tool -- where to start?

I'm currently a web developer with a backgound mainly in server side technologies however I've always had an interest in probability so recently I've been exploring building a dummy betting platform ...
787 views

### Predicting raffle winners

I don't have a strong background in statistics, so forgive me if I'm making very elementary mistakes here or if this question is too simplistic. I am in a club with ~80 members, and every week, 10 ...
1 vote
342 views

### What kind of results are there about prior knowledge?

Consider the following two problems: We want to do linear regression, where we know that the true model is actually linear. In the general case, linear regression includes an offset. However, we know,...
112 views

### calculating conditional probability-bayes rule

I'd like to calculate the conditional probability in the following case: I was told that a box contains a BLUE ball. this is my evidence, my prior probability of a BLUE being drawn is 0.3. and this ... 1 vote
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### How to to calculate the topic distribution of a document [closed]

I want to calculate Kullback–Leibler divergence on two documents. It requires probability distribution of each document. I do not know how to calculate probability for each document. Any simple ...
1 vote
355 views

### probability question

I would like to calculate the following conditional probability: I know that the probability of a BLUE ball being drawn is 0.3. I receive a message from A or B who saw the ball that has been drawn. ... 209 views

### Measuring probability that 2 sample originate from the same population

I have two dataset that i want to compare. each dataset contain the weight of 10 different person measured for 3 different day. I am interested in measuring the probabily that the two sample ...
1 vote
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### Calculating the probability that demographic trends happened by chance

I ran an ad campaign on Facebook and I have impressions (ad-views), clicks, and sign-ups broken down by gender and age. Certain demographics have a higher rate of clicks and sign-ups when compared to ...
153 views

### Probability of hitting tails [closed]

I have 5 variables for 1000 observations. Given the data, I need to Calculate probability of hitting top 5 pct in each of the distributions separately. For example, for the value of 123.45 I need to ...
5k views

### Computing Gaussian mixture model probabilities

I was looking over the solution to this question on SO and it got me thinking about computing probabilities for a Gaussian mixture model. Let's assume you've fit some Gaussian mixture model so that ...
123 views

### How to determine the statistical significance of a score from a general population?

Let's say I got a reading of 5 for a given measurement. For a random population, I got the following dataset of readings: ...
300 views

### Can I test the validity of a prior given data?

Problem I am writing an R function that performs a Bayesian analysis to estimate a posterior density given an informed prior and data. I would like the function to send a warning if the user needs to ...
13k views

### Time taken to hit a pattern of heads and tails in a series of coin-tosses

Inspired by Peter Donnelly's talk at TED, in which he discusses how long it would take for a certain pattern to appear in a series of coin tosses, I created the following script in R. Given two ...
25k views

### Normalizing constant in Bayes theorem

I read that in Bayes rule, the denominator $\Pr(\textrm{data})$ of \Pr(\text{parameters} \mid \text{data}) = \frac{\Pr(\textrm{data} \mid \textrm{parameters}) \Pr(\text{parameters})}{\Pr(\text{...
836 views

### Multivariate mutual independence test

I have a series of observations $\{X_i,Y_i,Z_i\}$ for random variable $X$, $Y$ and $Z$. Now I want to test if $X$, $Y$ and $Z$ are mutual independent, can anyone help me? Some pairwise independence ...
207 views

### Basic question regarding probability

I quote this question from "All of Statistics": Suppose a gene can be type A or type a. There are three types of people (called genotypes): AA, Aa, and aa. Let (p, q, r) denote the fraction ...
1 vote
2k views

### Odds for high in the card game pitch

In the card game Pitch how do I calculate when my opponents have 12 cards out of 52 if they have the Ace, King or Queen of a suit? I assume there is only about a 22% chance of the Ace being in their ...
140 views

### Probability of panel assignment

I am trying to determine the probability of a "mixed panel" assignment (i.e., a panel of judges w/at least 1 woman). Consider the following: A court has a total of 20 judges, 8 of whom are women. ...
297 views

### More info needed on second order regular variation in extreme value theory

My question is very general. I am learning extreme value theory to examine tail behavior. The concept of regular variation is still too vague to me. Could anyone help to provide more info to clarify? ...
1 vote
Repeating an experiment (about which I asked before) with $n$ possible outcomes $t$ times independently, where all but one outcomes have probability $\frac{1}{n+1}$ and the other outcome has the ...