# 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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### Probability distribution of functions of random variables?

I have a doubt: consider the real valued random variables $X$ and $Z$ both defined on the probability space $(\Omega, \mathcal{F},\mathbb{P})$. Let $Y:= g(X,Z)$, where $g(\cdot)$ is a real-valued ...
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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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### 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 ...
4k views

### 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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### Showing independence between two functions of a set of random variables

I've been working on the following problem and I'm confused about how to get started: Let $X_1, X_2,\dots, X_n$ denote i.i.d. real valued random variables, each absolutely continuous with an ...
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### How to Change prior probabilities for predicted variable in neural networks and other methods in SPSS Statistics

i am trying to find right model for predicting categorical variable with two values. Problem is that ratio of cases in group 1 and group 2 is not equal but rather in ratio of 2:1. When i try to find a ...
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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, ...
135 views

### Time series forecast with probability

I have historical data for a particular metric for each month for the last 3 years for different categories. The metric is a percentage and its heavily skewed towards 1 with more than 75% of values ...
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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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### Realization of a conditional expectation wrt a random variable

Let $Z$ and $X$ be a real-valued random variables. Is it true that $\mathbb{E}[Z|X](\omega)=\mathbb{E}[Z|X=X(\omega)]$ ? If so, why ? P.S : I'm looking for a rigorous mathematical proof, not ...
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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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### Probability Question - Mutual Exlusive/Independent (To the power)

A bridge has to be designed for a region which is subject to the influence of both floods and earthquakes. Its expected design life is 120 years. At the particular site, the probability of a flood ...
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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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### The effect size of difference

I have this interesting data where I would like to estimate possibly a parameter of the difference (between $A+B$ and $A+C$, inference using both) that would allow me to infer the development of $A$ (...
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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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### 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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### 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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### Multinomial distribution: probability that one outcome is greater than another

Consider a multinomial distribution with three outcomes. Let $x_i$ denote the number of occurences of the $i^{th}$ outcome, and the $i^{th}$ outcome occurs with probability $p_i$, $i=1,2,3$. Let $n$ ...
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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 ...
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: ...