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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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PMF and independence with two discrete random variables?

Each of n people (whom we label 1, 2, . . . , n) are randomly and independently assigned a number from the set {1, 2, 3, . . . , 365} according to the uniform distribution. We will call this number ...
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Distribution of the $L^{2}$ norm of a vector of components drawn from Gaussian distributions

I recently asked this question involving uniform distributions. I am wondering what would be the equivalent for Gaussian distributions. The problem states as follows. We consider a random vector $\...
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Return Period and Probability

My question is simple: If I assume that the probability to be hit by a lightning strike for a person in this year was 0.5 percent would it mean that if I was able to live 200 years I would be hit by ...
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Conditional Probability - Drawing balls from an urn

I have that question from a past exam (without answer): There are two urns, say I and II. Urn I contains 1 white ball and 1 black ball. Urn II containts two white balls and 3 black balls, and suppose ...
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Correlated Bernoulli Trials

Suppose there are $n$ dependent Bernoulli trials, $X_{1}$,...,$X_{n}$ with $% X_{j}\in \{1,0\}$ and $\Pr (X_{j}=1)=q$ for all $j=1,...,n$. For any $% n\geqslant 2$ dependent Bernoulli trials, in the ...
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Probability that a random voter voted for the same candidate twice

Let's say there are only two candidates(Candidate A & Candidate B) in an election and both of them ran for office in both elections. Candidate A received 48% of the vote in the first election and ...
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Find maximum likelihood given Rayleigh probability function

Problem Suppose we use a Gaussian PDF to express the likelihood of light intensity prevalent on Clear, Cloudy, and Eclipse weather. The probability of a certain amount of light value (positive or ...
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binomial responses in h2o gbm

I am modeling the probability of success in a dataset where I have a both the number of trials and the number of successes (and, obviously, I am modeling $p_i=\frac{total successes}{total trials}$). I ...
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Why is XGBoost prediction proba so concentrated within specific range? (unbalanced class)

I am pretty to new to Machine Learning. I am training on some past Kaggle competitions including the Santander Customer Satisfaction Challenge (https://www.kaggle.com/c/santander-customer-satisfaction)...
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48 views

Probability of each team placing in each position

I've been thinking about this for a while, and haven't been able to figure it out. My math teachers haven't been able to, either. You have N teams, and each team has P players. Each player plays a (...
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Beta-binomial distribution for scaled and translated Beta

Recall, that a binomial distribution in which the probability of success at each trial is randomly drawn from a beta distribution results in the so called beta-binomial distribution. One can calculate ...
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Bayesian Inference Toy Problem

Problem statement: Consider a probabilistic model where there are two states of the world, framed as complimentary events: $A$: All chocolates are black and $A^C$: 50% of chocolates are black. Let $p$ ...
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Connection between Hazard Ratios, Survival, and Probability

According to this wiki link, the hazard ratio relates to survival according to the following equation $$ S_1(t)=S_0(t)^r \quad (1) $$ where $S$ is the survival and $r$ is the hazard ratio. So from ...
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Must the domain of a CDF be $\mathbb{R}$ or can it also be a strict subset?

So my question is whether the domain of a cumulative distribution function has to be $\mathbb{R}$ or whether it can also be a strict subset. The reason I'm asking is because I'm currently going ...
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Calculate $P(b,c,a)$ if I only have a distribution probability table of $P(a,b,c)$

I have to calculate this: $P(b|c,a)$ I think $P(b|c,a) = P(b,c,a) / P(c,a)$ If I have this distribution probability table: How can I calculate $P(b,c,a)$ if I have $P(a,b,c)$? And I have also to ...
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Evidence fusion-Dempster Shafer

I have developed four models that estimate the same state-traffic volume in 100 streets during a specific time period. I have actual volume for 25 streets to estimate compute the reliability of each ...
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Different solution for a probability question

I got the following problem: Find the probability that for two arbitrary numbers $x$ and $y$ with $x,y \in [0,1]$ they satisfy $x+y<1$ and $xy<\frac1{10}$. In short words the sum of the two ...
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Unfinished game probability

I've seen recently this question on another site and gave it a try. There are $3$ players and a dice with $3$ unbiased faces let's call them $a$, $b$ and $c$. The first player bets on the face $a$,...
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How much “ground truth” data do I need to evaluate a heuristic classification approach?

I have a heuristic approach to a de-duplication problem: There are about 300 million unknown data points. I attempt to match each data point with one of about 4 million independently known data ...
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Comparison of extrapolated kaplan-meier survival curve with background mortality

For my research I am doing an health economic assessment of patients with a renal transplant. For my model I need to know their (yearly) mortality probability. My plan was to extrapolate survival data ...
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Random variables - proof of convergence in probability

I've got this exercise from lecture notes, but I couldn't find an answer. For each positive integer $n$, let $X_{n}$ be a non-negative random variable with $\mathbb{E}[X_{n}] < \infty$. Prove that ...
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Intuition behind gradient of expected value and logarithm of probabilities

I recently came across the following curious identity: $$\nabla_\theta \mathbb{E}_{x \sim D_\theta}[f(x)] = \mathbb{E}_{x \sim D_\theta} [ \nabla_\theta \log(D_\theta(x)) f(x)],$$ where $D_\theta$ ...
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Using Hoeffding's inequality to determine testing data size

Suppose one needs to perform binary classification on a dataset with 300 records of a random numerical variable, and need to ensure error rate on future data will not exceed the error rate on test ...
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What's a mean field variational family?

I'm working through variational Bayesian methods at the moment, and I think I have a grasp of the bigger picture. Where I sometimes have trouble is with the exact details of how it can be implemented. ...
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Looking for advice: Short-term forecasting using actual forecasts and real time data

First of all apologies, I have very little experience in statistics and my biggest problem is using the correct terminology. I'm here mainly looking for guidance and direction. Background: I have a ...
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Entropy/Measure of Knowledge for probability intervals

I have a system which outputs probability interval tuples over the decision set $\{d_1, d_2, d_3\}$, such that a tuple $([\min_1, \max_1], [\min_2, \max_2], [\min_3, \max_3])$ indicates that $\min_i$ ...
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Statistical test for first sample greater than given sample?

Does anyone know of a name for the following statistical test/whether there is a name/whether the following line of reasoning is just bogus? Say I have a value $x$, and a way to generate samples from ...
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Standard Errors of Probability

Can someone tell me how to calculate Standard Error belonging to a probability? I read somewhere about a relatively simple formula, but I am not quite sure whether this is correct. I am running a ...
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Statistical Reasoning of Noise Images on Random Pixel Generator

http://www.pixelmonkeys.org/#theory It is always explained that even billions of images are generated per second, it is almost impossible to see a natural image ( whether it is clear or distorted as ...
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Probability mass function of n dices thrown twice [duplicate]

You roll n dices independently from the other rolls. Than you roll again the dices that show a number other than 4. X = number of 4s. a. What is the kind of the distribution of X? What are the ...
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Checking if a coin is fair

I was asked the following question by a friend. I could not help her out but I hope someone can explain it to me. I could not find any similar example.Thanks for any help and explanation. Q: Results ...
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Expected time to visit all countries by random flight paths [closed]

Say there are $n$ different countries, the flight starts from some initial country. At each step, the flight can go to a random country other than the one where it currently is. The probability of ...
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Bayesian Probability question — Pointwise Probability

I am stuck in this question: if $a = 1$ then $m \sim U(0.2,1)$ else if $a=0$ then $m \sim U(0,0.5)$. The question is if $m$ is $0.3$ what is the probability that $a$ equals to 1? My thought is to ...
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Comparing ordering of sample and conditional distribution based on that sample

I don't have a specific question, but just a request for resources and/or guidance. Suppose we take $n$ draws from a distribution $F$. Suppose a particular sample is given by $\vec{\theta} = (\...
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Sufficient conditions for equal marginal medians

Let $X, Y$ be dependent random variables taking values on the same set (either a finite set, an interval or the real line). I'd like to know if there's any condition on $P(Y|X)$ which ensures that $$\...
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Best strategy to cheat on a lots game

Consider the game: 100 (n=100) people (inclusive you) are putting their names in a bowl for drawing a lot There is 5 (p=5) prices, thus 95 wins nothing Cheating You can just throw instead of 1 ...
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Distribution of the $L^2$ norm of a vector of components drawn from uniform distributions

We consider a random vector $\vec{v} = \left(x_{1}, x_{2}, \dots, x_{n}\right)$ built from $n$ real random variables drawn from a real continuous uniform distribution $\mathcal{U\left(a, b\right)}$, $...
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The probability density function of half-chi-square distribution

Let $X$ be a random variable from a chi-square distribution with 1 degree of freedom. The probability density function (pdf) of $X$ is $f(x) = \frac{\exp{(-x/2)}}{\sqrt{2\pi x}}$, $x>0$. In the ...
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Bound for type of correlation measure

Assume you have a finite, discrete probability distribution for a joint random variable and such that $P(X=i,Y=j) = p_{i,j}$ for $i \in \{1, \dots, |X|\},j \in \{1, \dots, |Y|\}$. The marginal ...
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How to calculate the probability that white will win a chess game?

I am developing a chess engine, and wrote four classifiers (logistic regression) for: detecting which part of the game it is (opening, middlegame, endgame) based on current board / position ...
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Equivalent way of rewriting a two-component mixture

I'm confused on the following equivalent way of rewriting a two-component mixture. Consider the two-component conditional mixture $$ F(z|x)=\lambda F_1(z|x)+(1-\lambda)F_2(z|x) $$ where all the $F$'...
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Probabilistic model: what's the probability of this model?

The above model is from Berkeley cs294-112 Page 23. It is said that $$ p(O_{1:T},s_{1:T}, a_{1:T}) =p(s_1)\prod_{t}p(s_{t+1}|s_t,a_t)p(O_t|s_t,a_t)\tag 1 $$ I'm quite confused about this solution: ...
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1answer
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Probability of drawing different items from a subset with replacement

I'm trying to generalize a game mechanic, to understand the probability that the game developers are giving us, but this went over my head. The mechanic is: draw 10 items from a bag of 33 items each ...
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38 views

Sum of square of gaussian random variable and exponential random variable

I have 2 independent RVs $s$ and $N$ with distribution as below: $\begin{array} { c } { f _ { s } ( s ) = \frac { 1 } { \sqrt { 2 \pi \sigma ^ { 2 } } } e ^ { - s ^ { 2 } / 2 \sigma ^ { 2 } } } \\ { \...
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What is the expected number of times you need to flip a coin before you see 2 heads? The heads do not need to be in a row

My attempt: The 2nd head must appear last in the sequence of k flips. Therefore the first head can appear in any of the first k-1 flips. The number of ways the first head appearing in the first k-1 ...
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In a set of 10 billion possible items, if I have X items what is the probability of two being the same? [duplicate]

If I have a device that displays a random number from 1 to 10 billion and I use that device X times, what is the probability that not all of the numbers displayed are unique?
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A 2 component mixture is symmetric if and only if $\lambda\in \{0,1,\frac{1}{2}\}$

Consider the following mixture of two densities $$ f(x)=\lambda g(x-\mu_1)+(1-\lambda)g(x-\mu_2) $$ with $\lambda\in [0,1]$, $g(\cdot)$ symmetric around zero, $\mu_1<\mu_2$. Claim: the mixture is ...
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What does Joint entropy really tells us?

I have two sequences of data A and B. A = [sunny, sunny, cloudy, rainy, sunny, sunny] with entropy 1.25 bits b = [hot, hot, cold, cold, cold, hot] with entropy 1 bits I have calculated joint ...
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Probability of mode value in a given series [closed]

I’m developing software which needs some math which is outside of my wheelhouse. I have a series of numbers, each single number in the series is submitted by a user. I want to determine the ...
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Probability question about panda births and statistical tests

I am self-learning statistics, and I have a question about how to do the following problem: There are two species of panda bear, A and B. Both are equally common in the wild and live in the same ...