Questions tagged [probability]

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

7,425 questions
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Bayesian updating - update probability that measurement is real

I have a sequence of observations, which are either a measurement of 'active' or 'inactive'. These measurements are not necessarily accurate, with false negatives being more unlikely than false ...
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I.i.d.-ness of some functions of random variables

I have some doubts on the i.i.d.'ness of some functions of random variables. The framework What I'm describing below is a simplied version of a well known model in economics of demand and supply. ...
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Have a question about bivariate random vector [closed]

When X follows beta (2,2) and X = x, the conditional distribution of Y is the binomial distribution B (15, x). The probability mass function P (Y = y) of E (X), Var (X), E (Y), and Var (Y) obtained by ...
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Which is faster: a bank with five lines of ten or one line of fifty?

I'm working on a probability question with mean and variance. Let's say that I have two banks. They are identical in every way, except that bank A has five lines with ten people each and bank B ...
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Collective name for properties including expectation, variance, divergences, etc

Is there an established name for the class of properties of random variables such as expectation, variance, higher moments, divergences (e.g. divergence). These are properties of one or several ...
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Why do we divide by the standard error when we evaluate sample statistics?

I'm reading Experimental Design and Data Analysis for Biologists by Professor Quinn and Profesoor Keough and, on page 20, they write - We can use the methods just described to reliably determine ...
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How much can I parse the results of an A/B test without breaking the assumptions in the test?

Let's say I run an A/B experiment on 1,000 rats. I give one group regular food and the other a special type of food that should help their cognition and I compare their performance at mazes. Imagine ...
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Probability of event independent of random variables [closed]

Let {$X_n$} be a sequence of independent random variables and for each $n$, the event $A$ is independent of $X_1$, $X_2$,..., $X_n$. Show that $P(A)$ is $0$ or $1$.
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Using R to calculate probability of rolling 2 numbers in 20 throws [closed]

We have an 8-sided die. Throwing it 20 times, what is the probability of rolling a number larger than 6 at least 12 times and at most 16 times? If you know of an efficient program to write so that I ...
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How is the formula for the entropy of the lognormal distribution derived?

Wikipedia gives the entropy of the lognormal distribution in nats as $$\mu + \frac{1}{2} \ln(2\pi e \sigma^2)$$ Can anyone point me to a derivation of this formula?
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Why Kullback-Leilbler divergence is a better metric for measuring distance between two probability distributions than squared error?

I know that KL-divergence is a metric that is more suitable when we want to measure the distance between numbers which a probability form. However, I am still confused what is the benefit of using KL-...
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How to characterize the effect of $(\textrm{Diag}(\Sigma^{-1}))^{-1}$ badly approximating $\textrm{Diag}(\Sigma)$

I have an almost singular covariance matrix $\Sigma\in\mathbb{R}^{n\times n}$ that has a few large eigenvalues, followed by many many comparatively very small ev's. If I were to try to approximate ...
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“At least” approximation calculation

I have a vector of different probabilities to get 1, for example probs = [0.1, 0.5, 0.2, 0.9, 0.25, 0.55] I have to calculate the probability of having at least ...
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Expected number of days?

You’re drawing from a random variable that is normally distributed $X \sim \text{N}(0,1)$, once per day. What is the expected number of days that it takes to draw a value that’s higher that two? ...
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Force sum of random varables to equal to 1 [duplicate]

Suppose I have 3 random variables, $X1, X2,X3$. Define $Z$ as: $Z=X1+X2+X3$ I want to force $Z$ to equal 1 for every "realization" of $X1,X2,X3$ ($X_i \sim Beta(a_i,b_i))$. As an example, let $X_i$ ...
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Sorry if this is too basic a question, or the wrong place to post. I am planning a road trip, and I'm trying to optimize the date I leave based on historically average weather for all the states I'll ...
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What is the probability of having a pair of doubles when throwing dice?

What is the probability of having a double (two dice will show the same number) when we throw 5 dice (all dice have 6 sides)? My calculations are: ...
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Looking for a name for theory of a “balance of fair probability” (example provided) [duplicate]

I'm looking for a name of topic(s), theories which describe the situation provided below: Let's say we have a 6-sided fair dice. And after 6000 throws we have the following results: Digit 1: 1145 ...
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Expectation over a max operation

Let $X \in \mathbb{R}_{\geq 0}$ be a "non-negative" random variable and $c$ is a "given" strictly positive number. I wonder if the following inequality holds: $$E[\max\{X,c\}] \leq \max\{E[X],c\},$$ ...
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what is difference between $95 \%$ CI of mean and 95% pdf of normal distribution?

We took sample mean $\mu = 14$, and $\sigma = 0.45$. Calculate required area of normal distribution We will apply $\int_{13.19}^{15} f(x) \ dx = 95\%$. 95 % CI of mean But if we took sample size ...
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Predicting elections: Probability distribution from betting odds and dependence

Suppose I want to find the percentage of votes each party will get in elections. I have following odds from betting companies. My first thought is to find the probability for each party achieving a ...
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Can independent/dependent events be thought of graphically?

My understanding is that events are subsets of the total outcomes in a sample space. So if two events are mutually exclusive, then they (the sets) do not overlap in the sample space. This can be seen ...
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What are the main approaches to the foundation of statistics without probability

The frequentist, likelihood and, to an even greater extent, Bayesian approaches to statistics are all based on probability. Without probability, it seems difficult to use a data sample ("seen" cases), ...
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sum rule in conditional probability

P and S are the common cause of c. If P(C=true| P,S ) is given , can I introduce S to P(C|P) as P(C= true|P= true)= P(C=true| P =true , S= true)* P(P=true ,S=true )+ P(C= true | P=true ,S =false )*P(P=...
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Probability of association in logistic regression models

I’m using a logit model to evaluate the association of a set of habitats (H) to a particular land cover. Both land cover and H are binary variables. ...
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How to derive a ranking function from observations

I have a employee dataset with the following 5 details. projects completed customer ratings number of bugs reported customer complaints profit I want to rank ...
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Predict Taking a Loan

I want to build a Logistic Regression model to help me predict taking a loan by a customer base on several variables. I started building a data set for the customers who already took loans and some ...
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Unusual Markov inequality for normal distribution

I'm trying to answer the following question from Larry Wassermans book on statistical inference. My question is how did they arrive at the Markov bound, it does not seem like the normal form of the ...
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survival probability to proportional hazard ratios in r

I am using Cox proportional hazard regression to determine the association between physical behaviors (physical activity, sedentary behavior, and sleep) and mortality. to elaborate on these results, I ...
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Bayesian chi-squared tests

I have a dataset with two groups of participants. Each participant performed a repeated measures task on which three types of errors could be made. I want to measure the difference in distributions of ...
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KL divergence between gaussian and uniform distribution

Is the KL divergence not defined because uniform has bounded support and gaussian has unbounded support? How else can I calculate the distance of my gaussian to a 'maximum entropy' distribution if I ...
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Probability of seeing a bird on a certain date based on historical notes

I have a database filled with different bird species that were seen on different dates (10 years of records). Each row in the table contains: Date, Time, Bird Species, Spot where it was seen So it ...
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Why does discrete data distribution has differential entropy of negative infinity?

Recently I've been reading a paper. In section 3.1, it says "Since the discrete data distribution has differential entropy of negative infinity, this can lead to arbitrary high likelihoods even on ...