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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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Probability of userbase recieving special page

Say I have an app. When the app is launched there is a process behind the scenes the determines which of the two outputs the user receives, default or special. The default output displays the app ...
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Proof of probabilities that may not be independent

I am given the problem: Given $P(A) = \frac{3}{4} $, $P(B) = \frac{3}{8} $, show that: a) $P(A or B) > \frac{3}{4} $. b) $\frac{1}{8} < P(A and B) < \frac{3}{8} $. The problem does not ...
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bayesian decision making - comparing expected loss

The problem is like this: Suppose that I am considering which country should I invest on, country A and country B, based on their GDP growth rate $\alpha$. There are two possible choices for each ...
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1answer
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How to estimate the probability distribution of two parameters given a discrete output?

I'm currently facing a new type of problem, and i have no idea how to solve it, so any suggestion will be really appreciated ! The problem is the following: I have a matrix of temperatures, depending ...
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differences between conditional probability and dependency

Sometimes, I read articles about conditional probabilities and other articles about conditional dependency. My question what is the main differences between them? For example, "https://en.wikipedia....
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Independent Study Statistics/Probability Grad Level [duplicate]

I am trying to decide on topics for my independent study this semester. I am a Pre-Doctoral Mathematics student, so looking for a more math based text rather than engineering based (which I have found ...
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Co-occurence in a population

Let's say I have a population of size N that has traits a-z. Some people/samples might have just a,n,x, etc... P(a), ..., P(z) is known. # of people with i & j in the population is known for all ...
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Series Winner Probability

Suppose we have Series 1 and Series 2, and four teams $A,B,C,D$. $A$ and $B$ play in Series 1 and $C$ and $D$ play in Series 2. In each series, the first team to win 3 games wins the series. The home ...
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Probability Winning Game [duplicate]

Suppose you are tied $1-1$ with Bob. To win the game, you have win greater than or equal to $5$ rounds and win at least $2$ more rounds than your opponent. The probability of winning a round is $40\%$ ...
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Probabilistic user behavior markov models on web [on hold]

I am considering the following probabilistic Markov model of actions of a user on the results page of a search engine. The user examines the first result, with a probability $A$ he is satisfied with ...
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Find the distribution function $F$ for $min_{1 \le i \le n}{X_i}$ [duplicate]

Given a random sample $X_1, X_2, ..., X_n$ where each $X_i$ has pdf: $$ f(x; \theta) = 3 \theta^3 x^{-4} $$ and $0 \lt \theta \le x \le \infty$. Show that the distribution function $F$ for $min_{1 \...
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Sufficient conditions for multivariate MGF to be finite in neighborhood of zero

In the one-dimensional case, we have the following fact: (see Existence of the moment generating function and variance for proof) Proposition: The mgf $m(t)$ is finite in an open interval $(t_n,t_p)$ ...
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NFL Playoff Game Probabilities

Context: My friends and I have this homebrew NFL fantasy football game we play for the playoffs once the NFL regular season is over. The contest is not head-to-head with other players like standard ...
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2answers
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What does $\sum_{\{\textbf{x}:T(\textbf{x})=t\}} f(\textbf{x}; \theta)$ mean?

This is in the following context: $$ q(t;\theta) = P(T=t;\theta) = \sum_{\{\textbf{x}:T(\textbf{x})=t\}} f(\textbf{x}; \theta) $$ Where $T=T(\textbf{X})$ is a statistic, $q(t; \theta)$ is the pmf of ...
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Is the sum of one slowly varying and one regularly varying random variable regularly varying?

Imagine I have given a random variable $X$ with support $\geq 0$ and $\mathbb P(X=0)>0$. Also, I have another independent random variable $Y$ with positive support being regularly varying at zero ...
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Is the sum of two dependent sub-gaussian variables X and Y still follows sub-gaussian distribution?

I am trying to prove the random vector with dependent sub-gaussian coordinates is also a sub-gaussian random vector. The related question has been asked in https://math.stackexchange.com/q/3072363/...
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2answers
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How can we best explain causality for the uninitiated?

How can we best explain causality in layman's terms? There seem to be two main types of causality. One is probabilistic causation, the other is called determinism in philosophic circles or just ...
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How to find the value for average rate

I'm doing some textbook problems on my own and there are no steps given to the solutions to some of the problems. If anyone could help me solve the following problem, much would be appreciated. "A ...
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1answer
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Compute $P(2\leq x\leq 8)$ with Poisson distribution and $\lambda=7.2$

Compute $P(2\leq x\leq 8)$ with Poisson distribution and $\lambda=7.2$ My attempt: I need calculate this using $R$. then I use this: ...
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Writing down a conditional probability / finding the underlying probability space

This is a notational issue: Let's say we have a partition of $\mathcal X$ given by $\{\Omega,\Sigma\}$ and we define $P(\omega\in\Omega) = p$, $P(X(\omega)=x|\omega\in\Omega) = \pi$ and $P(X(\...
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Recursive Bayes Learning

I'm trying to work through an example from Richard Dudas Pattern Classification on Recursive Bayes Learning. My main question is why do we choose the $max[D^n] $ in: $$max[D^n] \le \theta \le 10 $$ ...
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Probability with or and under in the questions [on hold]

Can anyone please help me to solve these problem with explanation as possible.
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doubtful regarding my solution to bonferroni's principle exercise

Self learning and not quite good at probablility and statistics, my question is regarding solution to exercise 1.2.1 in chapter 1 of Mining of Massive Datasets book. The text of the exercise reads: ...
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1answer
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Probability of finding a lost item

I am trying to solve the following problem and was wondering if someone can verify my answers. Big Joe has lost an important document. There is a 70% probability it is at home, and a 30% chance it is ...
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probability sampling for retrospective chart review RCR/Medical Record Review

how best can you achieve probability sampling in a medical record review. In answering question, please use a real example. Say you have 4000 pregnancies to review, how many of these do you need to ...
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1answer
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Conditional Probability: $\mathbb{P}(B/A) \geq \mathbb{P}(B)$ [on hold]

Let $A$ and $B$ be events associated with a probability space $(\Omega, \mathbb{A}, \mathbb{P})$. Prove that (a) if $\mathbb{P}(A/B) \geq \mathbb{P}(A)$, then $\mathbb{P}(B/A) \geq \mathbb{P}(B)$; (b) ...
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States of Markov chain and stationary distribution

Let $X$ be a Markov chain with a state space $S={\{0,1,2,... \}}$ and a transition matrix $P$ with given $p_{i,0}=\frac{i}{i+1}$ and $p_{i,i+1}=\frac{1}{i+1}$, for $i=0,1,2,...$. Find out which states ...
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Classic probability for contradicting information

We are currently trying out a statistical approach for user attribute confidence on user data, based on different sources providing this data. As an example, let's say we build this initial ...
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18 views

Infimum of the difference between KL Divergence and Entropy [on hold]

Suppose $y_1 = 1, y_2 = y_3 = ...=y_n = 0\ (n\geq2)$, and $\sum_{i=1}^np(y_i|x;\theta) = 1$, $0\leq p(y_i|x;\theta)\leq1$. Meanwhile $\alpha > 0$ is a constant. Let's define a function $$f(\theta)...
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Can anyone give a answer to the floowing [closed]

The heights of children two years old are normally distributed with a mean of 80cm and a standard deviation of 3.6cm. Pediatricians regularly measure the heights of toddlers to determine whether there ...
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Probability that exactly 12 buses will arrive within 3 hours

Let's suppose there are two buses $A$ and $B$. They draw up at the bus stop under the Poisson distribution with intensities $3$ and $5$ times per hour. (a) What's the expected length of time after the ...
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Probability Mass Functions [on hold]

In a bowling "frame", between 0 and 10 pins might be knocked over by a bowling ball. Suppose that a particular bowling alley attracts a mixture of beginners and experts, such that we can assume that ...
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I am confused between selection of limits for joint distribution [duplicate]

I am given the following joint distribution of two random variables X and Y: $$ f(x,y)=2y \\ 0<y<1, 0<x<y $$ Now I need to find the marginal PDF of X but how do I ...
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Proving that given Markov chain is homogeneous. Find state space and transition matrix

Let $X_i$ be the results of a consecutive throws of a die. Let $Z_n=3(X_1^2+\cdots+X_n^2) \bmod 5$. Show that the sequence ${\{Z_n \mid n\geq1\}}$ is a homogeneous Markov Chain. Find a state space and ...
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Probabilistic Interpretation of Radial Basis Function

I was wondering if someone could flesh out the probabilistic interpretation of using the Radial Basis Function to compute the probability between an observation and some reference value. My question ...
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Reinforcement learning with two goal states [closed]

I implemented my first TD off-policy method for discrete states and discrete actions (increase or decrease to last executed action) on a patient in real time. Now I am extending my problem from one ...
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Continuous Stochastic Processes examples

I am trying to understand various types of stochastic processes. In order for that to happen, I needed some simple examples to be built so that I can build an intuition about them. According to the ...
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1answer
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What is the formal name of the following problem: predicting next output based on previous values, NOT a sequence

I have a system producing an output periodically, I would like to build a model to predict the next entry. There is no sequence relation between the output values, order doesn't matter. The only ...
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2answers
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Confusion in modelling finite mixture model

From the book "Machine Learning a probabilistic Perspective", I'm reading about finite/infinite mixture models. Particularly at paragraph 25.2.1 it's stated: The usual representation (of a finite ...
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Expected number of steps in Gambler's ruin game with two players

Let's say we have two players A and B. Player A has 3 coins and player B has 5 coins. If player wins the other player gives one coin. During game second player probability of loosing is $2/3$, while ...
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1answer
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Is the sampling distribution of a complete sufficient statistic free from relevant subsets?

Let $T_{\theta}(\mathbf{x})$ be a complete, sufficient statistic $T_{\theta}: \Omega \mapsto \mathbb{R}$, where $T_{\theta}$ is indexed by the parameter $\theta \in \mathbb{R}^n$. Is it true that the ...
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Resources for prerequisites to Probablistic Machine Learning Models

I am a self-learner and have done several machine learning courses but diving into Bayesian or Probabilistic Graphical Models I feel like my prior knowledge is inadequate. I have done some Probability ...
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1answer
31 views

Multi-dimensional CDF on a discrete support

Suppose I have two discrete-support random variables, $X$ and $Y$. They have joint CDF $F(X,Y)$. If I want to find $\Pr(a \leq X \leq b , c \leq Y \leq d)$. It is obviously not: $F(b ,d)-F(a-1 ,...
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1answer
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Computation within log space

What is the conversion of the following equation into log space? $bf2 = 1 + (p * (bf1 - 1))$ Given log.bf1 (log Bayes factor), how do I get to log.bf2 without having to compute bf1, but instead ...
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Discrete Stochastic Processes examples

I am trying to understand various types of stochastic processes. In order for that to happen, I needed some simple examples to be built so that I can build an intuition about them. According to the ...
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0answers
30 views

Some simple examples to understand various types of Stochastic Processes

I am trying to understand various types of stochastic processes through some analogical examples using simple experiments like a coin toss or die roll. The book of Hwei Hsu (Chapter-5, Page-162-165, "...
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2answers
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How do you multiply two conditional probabilities?

I have to multiply this: $P(a|b,c)·P(b|c)$ How do you multiply those two expressions? It seems that $P(a|b,c)·P(b|c) = P(a,b|c)$ but I don't know how to obtain that expression multiplying the two ...
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Fitting hedge fund returns to theoretical probability distributions

I know that a lot of work has been done characterizing the first four moments of monthly hedge fund returns across a variety of fund types and strategies, and that work indicates that the higher ...
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1answer
59 views

Genomics Stats Problem

I have used a python script to identify target sequences in a DNA sequence file. There are two classes of sequence: coding and non-coding. I have identified 728 sequences of interest. 597 of these ...
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Probability of deviation of percentages

In a set of N individuals X% have some characteristic. In a random subset of M individuals of this set, we observe that Y% have the characteristic. Note that M is not necessarily very small compared ...