# Questions tagged [probability]

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

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### Marginal distribution of a Poisson rate

I have a random sample of Yi~Poisson(θ) with i=1,..,n. Where I assume a gamma(a,b) prior for θ. Where I'm able to find the marginal distribution of Y to be a NegativeBionomial(a,p) where p=(1/(1+b), ...
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### How the variance of a potential loss X has been derived

I'm studying Insurance and I have a question about how the variance has been computed in this example. Imagine a case where an "agent" may suffer a loss, because of an event (an accident) occurring ...
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### Basic probability question in microeconomics [closed]

There are two players in a gamer N={1,2}, their actions lay between a=[1,infty) and their type lays between [0,200]. given that x is within [0,200] and P(t_2 < x|t_1)=x/200 (the type of each player ...
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### Factorization of the Characteristic function for sum of dependent data [closed]

We know that for $S_n=X_1+X_2+...+X_n$ the characteristic function is $\mathbb{E}_X\left\{\exp(iuS_n)\right\}$, where if $X_1 ,X_2 ,..., X_n$ are independent, it can be expressed as follows \begin{...
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### Understanding three prisoners (Statistical Inference - Cassella and Berger)

There are quite a few questions regarding three prisoners riddle, but my question relating to a particular line of reasoning from Cassella and Berger, as highlighted in the image below. Could you ...
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### Extendability of finite sequences of exchangeable random variables?

The old paper Binomial Mixtures and Finite Exchangeability by G. R. Wood makes reference (see Table 2) to a 1971 conjecture of Crisma that gives a formula for the probability that an exchangeable ...
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### Expectation of 500 coin flips after 500 realizations

I was hoping someone could provide clarity surrounding the following scenario. You are asked "What is the expected number of observed heads and tails if you flip a fair coin 1000 times". Knowing that ...
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### Combinatorics and probability

I have 7 interviewees and 14 interviewers. Each interviewee is interviewed by 4 of those 14 interviewees. Is it possible to have every interviewee to be shared by at least 1 interviewer, as to allow ...
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### What information in general is necessary to fully specify a multivariate distribution?

Given some multivariate probability distribution, we can fully describe it with its density or mass function -- we can associate each point in the space with either a probability density or mass, ...
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### Obtaining valid win probabilities from contest data using a binomial model

I conducted an enclosure experiment on lizards where I recorded contest outcome for every male-male combat. We had three morphs of lizards (o, w, y) in each enclosure. I am interested in obtaining ...
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### Logit - probit regression

I was running regression of - determinants of acceptance into a social science college. I found this unrelated paper (Screenshot of relevant page attached herewith). Here, they have computed logit and ...
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### Finite Mean and Finite Variance [duplicate]

Let $X$ be a random variable. Suppose there exists a constant $c ∈ R$ such that $E(|X − c|^2) < ∞$. Show that the random variable $X$ has finite mean and variance. And I'm quite confused about the ...
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### One-way ANOVA method validation

Here is my case: Let's say we have 50 polygons(looks like this:and a point set distributed within these 50 polygons. So that for each polygon, there is an associated point density. What I want to ...
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### How many losing runs of length r playing x numbers in roulette in a sample of n bets?

A losing run is defined as a number of consecutive losing bets. I've written a program to simulate this but the results I'm getting are different from what the formula gives, so one or another is ...
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### How many times would you need to watch a movie to have seen every moment of it (i.e. not blinking)?

Say we blink stochastically for .1 seconds every 4 seconds on average. How many times would we need to watch a 120 minute movie (assuming your eyes are glued to the screen the whole time), to have a ...
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### Where is the measure theoretic probability theory actually applied?

Where is measure theoretic probability theory actually applied? I've done quite a bit of graduate work in machine learning, Bayesian machine learning, information theory, and statistics (both ...
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### Calculate conditional probability using sample from 3variate normal distribution

I am working in R and have a matrix (200X3) named X where I have simulated data from a 3variate normal distribution given its parameters (variance-covariance matrix & and mu). My task is to ...
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### How high is the probability that copy N bytes of data from /dev/random to a file will result in a working application? [closed]

After talking with some colleagues, a question came up about the probability of copying N bytes from /dev/random to a given file on disk (either creating a new file, or truncating and overwriting an ...
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### Expectation of the k-th order statistic of a standard Gaussian sample

Let $(X_1,\dots,X_n)$ be independent random variables with common distribution $\mathcal{N}(0,1)$. The order statistics satisfy $X_{(1)} \leq X_{(2)} \leq \dots \leq X_{(n)}$. I am interested in the ...
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### How to rank data based on cross-validation

I had this problem from a long time. I have small dataset with about 1000 data points. The data is labeled as 1 or 0 (i.e. ...
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### Estimation of generalized gamma convolutions

How can i estimate on a data sample parameters of a generalised gamma convolution ? To be more specific, if my estimation gives me only a gamma convolution and not a generalised gamma convolution i'll ...
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### Range of probability for non-independent events

Suppose the probability of rain on day 1 is $p_1$ and probability of rain on day 2 is $p_2$. Then the probability of rain for the entire two-day period is $1-(1-p_1)(1-p_2)$, under the assumption that ...
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### Understanding t bounds on MGF

I'm having trouble understanding what the bounds of the $t$ variable are for an mgf. My questions are bolded. Here's an example from a textbook: Suppose X is a random variable for which the pdf is: ...
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### How to change the distribution of classes?

I have two classes [0,1] and I want to evaluate algorithm on different distributions of classes. I did label flipping incrementally such as 0%, 10%,20%,....,90%,100%. Does label flipping change the ...
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### Moment of a function of Gaussian random variables: $\mathbb{E}[(a_{i}^{\top}AA^{\top}a_{j})^{q}]$

Let $A$ be an $m\times k$ matrix with iid $\mathcal{N}(0,1)$ entries and $a_{i}$ and $a_{j}$ be its $i$th and $j$th columns. I would like to compute the following quantity: \begin{equation} \mathbb{E}...
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### Probability density function analysis question

The distribution(normally distributed) of the amount of money that people withdraw from an ATM has an average of \$70 with a standard deviation of \$10. If a group of 15 people withdraws money in a ...
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### Determining the degree of confidence of a Prediction

I'm handling a text multi class classification problem using RNN LSTM and model is pretty accurate (approximately 95%). But I'm interested in finding the degree of accuracy of a Prediction. Can I make ...
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### Stochastic Models (probability)- simple symmetric random walk question

My study group and I are currently stumped on this probability question related to Stochastic models. Let {Xn} be a simple symmetric random walk (ie p = 1/2). ) Give an approximation of the ...
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### How do you prove that samples are equally distributed even when taken without replacement? [closed]

I was reading Casellar and Berger's book and came across this well-known property. Although, in the book, the proof for any Xi is not provided. Does anyone know how to follow up on it? I'm curious, is ...
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### What prior would lead to $\ell_\infty$ regularization of model weights?

Gaussian prior on weights of a GLM lead to Ridge / $\ell_2$ squared regularization. Laplace prior leads to $\ell_1$ regularization Question What prior would lead to $\ell_\infty$ regularization ?