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

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Quantifying the error from a Bayesian model

I have a Bayesian model that predicts the chance of some event occurring. To view the accuracy, I took the prediction output of my test data and binned it every 10%. For example, if the model ...
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1answer
22 views

Expected number of trials - Bayesian

ref: 2.11 Question 2. Gelman et al.: Bayesian Data Analysis 2nd ed Consider two coins, $C_{1} \text{ and } C_{2}$ with the following characteristics: $Pr(heads|C_{1}) = 0.6$ and $Pr(heads|C_{2})$ = ...
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0answers
17 views

Convergence in Probability to a Constant [on hold]

Let $X_{1}...X_{n}$ be a sequence of random variables that converges in probability to a constant a. Assume that $\mathbb{P}(X_i > 0 ) = 1$ for all $i$. Verify that $Y_{i}=\sqrt X_i$ and $Y_{i}^{'} ...
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1answer
36 views

What is the expected value of the expected of x conditional of y? $E(E(X|Y))$ and also if possible $E(X^2|Y)$?

What is the expected value of the expected of x conditional of y? $E(E(X|Y))$ and $E(E(X^2|Y))$? I was doing this question. And got this result. But got stumped at the next question. Which asks me to ...
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19 views

Convert probabilities of “binomial events” into beta distribution for binomial parameter (theta)

I have three events that essentially arise from a binomial distribution with k=2, i.e., X~Binomial(theta,n=2). Given some model and data I obtained a conditional (pos distribution for a particular ...
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0answers
13 views

Model Perplexity explanation

Not sure if this is the place to ask about model perplexity. I have googled some explanations but it does not seem to yield much results besides the wikipedia explanation. Can someone explain to ...
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0answers
20 views

State the distribution of the time he has to wait for four customers to arrive. Sketch its density and calculate mean and variance of the waiting time [on hold]

Lim operates a long-distance taxi service from the central bus terminal in Kuala Lumpur to Seremban, a town 60 km away. Customers arrive at his taxi stand at an average rate of one every four minutes ...
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8answers
3k views

What's the name for this statistical fallacy?

I was told an anecdote by someone today who was trying to prove a point regarding safety. They said "50 people have been living in [area a] for the past two years one year (apparently I remembered the ...
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2answers
67 views

The frequency in histograms

My question is trivial, but the problem is that I found contradictory answers on internet. So I have the following sample data: ...
4
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2answers
94 views

Inference on $P\left(\left.\sum_{i=1}^{N}X_{i}\ \right|\ \sum_{i=1}^{N}X_{i}^{2}\right)$ when $X_{i}\sim\mathcal{N}\left(0,1\right)$?

Let: $$X_{i}\overset{i.i.d}{\sim}\mathcal{N}\left(0,1\right)$$ Hence: $$\sum_{i=1}^{N}X_{i}\sim\mathcal{N}\left(0,N\right)$$ and $$\sum_{i=1}^{N}X_{i}^{2}\sim\chi^{2}\left(N\right)$$ What can ...
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0answers
33 views

Linear model with proportions as the dependent variable

I have a linear model where the dependent model is a proportion (or a probability). I know I should probably use another type of model, and I am. I would still like to use also a linear model because ...
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2answers
490 views

How frequently am I going to lose this game?

I hope this question fits the site, if not feel free to flag. In the place I live there's a simple game of cards that you play on your own. Cards are 40, let's say A1 ... A10 , B1 ... B10 , C1 ... ...
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1answer
34 views

Roomshare - avoiding the worst choice

I'm moving in a new shared house with two other people. There are three bedrooms in the house and we will draw numbers from a hat for the rooms. All agree that room one is better than room two and ...
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0answers
23 views

calculating probability when given three possible outcomes [on hold]

let A denote the event that a student chosen at random fails accounting and B the event that they fail statistics. suppose P(A)=0.2 P(B)=0.15 P(B/A)=0.7.find the probability of failing statistics and ...
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1answer
33 views

Survival Analysis/Frailty Model

I am trying to build a probability model for the following situation: I have a very large dataset, whose rows are users and columns are the features. All the users visit a particular store X (once ...
7
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1answer
99 views

How many sides does a die have? Bayesian inference in JAGS

Problem I would like to do some inference on a system analogous to die with an unknown number of sides. The die is rolled several times, after which I would like to infer a probability distribution ...
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0answers
11 views

Loss Size Index Function of A Lognormal Random Variable

I have this tutorial question and I've gone through the solutions, getting all but one line of working. I broke down the question to this point but I can't seem to get out the following. So Loss Size ...
7
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1answer
77 views

Distribution of the exponential of an exponential random variable

Let $X$ be a real valued random variable with exponential distribution. Let $a$ be a complex number. What is the distribution of $Y = e^{aX}$? Can Y be written in the form of another known ...
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0answers
12 views

Statisitcal Probability of matching single dights [on hold]

I am trying to find the possibility of matching a string to digits 1,9,6,7 The potential values are 1-9. If the string does not match one of the four values I will modify the string to see if the ...
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3answers
67 views

Number of combinations from a set with certain rules

Suppose I would like to select $m$ integers from the set $S=\{1,2,...,n\}$ with the following rules: 1) $j$ out of $m$ are necessarily distinct. Denote this as $S_1$ 2) the rest $m-j$ are selected ...
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1answer
52 views

Probability Density Function of the derivative of a stochastic process? [on hold]

Suppose x(t) is a random process (RP) and we know the statistics of this random process completely e.g. its pdf (probability density function) and higher order statistics. The time-derivative of the ...
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1answer
24 views

Correct Method: Scale emprical CDF or best fit CDF

I have some data, with max value $M$. I assume it is sampled from some distribution with infinite support. A best-fit CDF is calculated $F(y)$ and so is an empirical CDF $F_{N}(y)$. My issue is that ...
2
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0answers
33 views

Binomial Distribution With Scale Variable?

I'm attempting to generate some random data using a distribution. I need each random point to fall within a certain range e.g. 0-20, and I would also like to control where the center of the curve ...
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1answer
30 views

what is the intuition behind the SRSWOR formula?

I earlier asked about Slovin's Formula (http://math.stackexchange.com/questions/1410492/what-is-the-intuition-behind-slovins-formula), and learned shortly thereafter that it was derived from this ...
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21 views

Are the $\text{P}$ and $\Pr$ operators equivalent?

I have seen both used to represent probability. Are they interchangeable?
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0answers
34 views

Suppose the ln(odds) of an event is -0.42. what is the probability of that event?

I have found the value of odds = e^-0.42 and I know the formula for finding odds is p/(1-p). However, The answer used the equation p/(1+p). Can anyone explain this to me?
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1answer
20 views

Analytical expression for variance as a function of the mean value

I have a research problem that seems analogous to a 'draw balls from a bin' problem. Imagine an experiment where $N$ balls are drawn from an infinite bin containing '0' balls and '1' balls, where $N$ ...
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0answers
12 views

CPD Logical OR - context-specific independence [closed]

$X_1$ and $X_2$ are the parents of $Y$. $X_1$ and $X_2$ are two independent Bernoulli random variables. $Y = OR(X_1, X_2)$. Are $X_1$ and $X_2$ context-specific independent when $Y = 0$? By knowing ...
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1answer
60 views

Conditional probability: how do i find the conditional probability given two parameters?

It is known that 25% of full time workers are also students. It is also known that 64% of the population work full-time and that 22% of the population are students. If a member of the population is ...
2
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0answers
28 views

convergence rate of Pearson correlation matrix

I posted recently a related question about the convergence rate of a Pearson correlation coefficient, here. Now, I am interested in the matrix version. Let $X_1,\ldots,X_N \sim \mathcal{N}(0,1)$ be ...
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18 views

Probability of a team scoring a goal?

I am trying to work out the probability of teams scoring a goal in a football match. Obviously there are many factors to consider, and the probability is impossible to predict correctly as there are ...
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1answer
62 views

Role of probability in machine learning

In any machine learning example say linear regression, the objective is sometimes two-fold. One to optimize some analytical function like squared error and one is to optimize some probability ...
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1answer
30 views

Probability homework question with specifity, sensitivity and prevalence

Assume that a diagnostic test for EPM (equine protozoal myoeloencephalitis) has a sensitivity of 89% and a specifity of 92%. The prevalence of the disease is 1% What is the probability that ...
3
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2answers
65 views

Probability of a run of events from past data

I would like to calculate the probability that there will be a car crash at a certain crossroad for three days in a row. I would like to compute that based on the data I have about the crashes in the ...
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0answers
19 views

Which regression model to use for a probability as dependent variable? [duplicate]

My dependent variable is a probability. As such, values lie between 0 and 1. The most common values are 0, 0.5, and 1 each occurring in 20% to 30% of the observations but any value in between is ...
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2answers
41 views

Conditional Probability of Bathroom Stall Availability

You're walking towards a bathroom which has two stalls, Stall A and Stall B. There can only be two people in the bathroom at one ...
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0answers
12 views

Good way to weight some data based on inverse probability of occurence

I am trying to weight some observations from some data (this kind of thing is new for me). Basically it is observational data not designed as a weighted survey, but I want to use inverse weights to ...
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0answers
17 views

What is the point of finding a representative sample distribution rather than calculating the probabilities directly from the sample?

The only advantage I can see is in using things like confidence intervals determined from the distribution, but I constantly see people fit a distribution to a sample and use that to calculate the ...
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0answers
14 views

Local Version of Bernstein Von-Mises Theorem?

The Bernstein-Von Mises theorem says that, under reasonable conditions, the posterior distribution $p(\theta | x_{1},\ldots,x_{n})$ converges weakly to the normal distribution after suitable ...
2
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0answers
42 views

Stories about statistics, machine learning and data mining [closed]

I'm looking for interesting stories about statistics, machine learning, etc. Examples of stories I find interesting are the following: https://en.wikipedia.org/wiki/Carl_Friedrich_Gauss developed the ...
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23 views

probability of random sample mean

company x - mean life time: 6.5 variance: 0.81 company y - mean life time: 6.0 variance: 0.64 what is the probability that a random sample of 36 from company A will have a mean life time that is at ...
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1answer
22 views

How should I model this infection spreading problem? Is this article's solution at all reproducible?

While on the internet, I came across this quote in a Buzzfeed article, which granted, is probably not going to be the height of journalistic quality at all: This is simple math. If one person ...
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1answer
60 views

Probability of an unknown distribution

I have the sample of a variable $X$ whose distribution is unknown and I would like to know how to estimate the probability of $X$ taking some values. How can I do that? I assume that there's a non ...
0
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1answer
21 views

Simple Probability: Comparing marketing campaigns with pre and post-marketing data available

I have 5 campaigns and 3.000 people who took part in it, my data consists of people who took part in the campaign and then another measure 6 months later that shows how many of them converted. I want ...
3
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1answer
133 views

statistics of airline crashes

Ive been going back and forth with a friend of mine on the issue of airline crash statistics. The concept of "independent variables" seems to be the biggest disagreement between us, so I was hoping to ...
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1answer
33 views

Calculate probability of event from ecdf in R

I'm using R and would like to calculate the probability of an event happening. I used the ecdf function on daily revenue (month-to-date). I have a target and a daily number necessary to hit target ...
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21 views

Compute the Gibbs energy

I have a question about Gibbs distribution in Stochastic theory. In which, it defined a clique as a a subset $C$ in the whole image $\Omega$ if two different element of $C$ are neighbors. Figure 2 ...
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1answer
92 views

What is this random number generation algorithm and why does it work (or does it)?

Found the following (Monte Carlo) RNG algorithm in a certain article. Let $f(x),f:\mathbb{R}^n \rightarrow \mathbb{R}$ be the function from which the samples are desired. Draw a random point $x \in ...
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37 views

integral probability transformation

I have a data matrix and I want to get samples from the distribution that each row has by integral probability transformation method. I don't know what should I do? Any idea about it?? Here I have put ...
4
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1answer
82 views

Is there something clever I can do with a log of a sum?

In something I'm working on, the expression $$\lim_{n\rightarrow\infty}\exp\left(-\frac{1}{n}\log\left(\prod_{i=1}^{n}X_{i}+\prod_{i=1}^{n}Y_{i}\right)\right)$$ came up, in which all $X_{i}$ $iid$ and ...