The probability that an event A will occur, when another event B is known to occur or to have occurred. It is commonly denoted by P(A|B).

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Connecting vertices in a graph stochastically. How to calculate a joint condition?

Full disclosure: I've posted this on reddit at /r/askstatistics, but haven't gotten any feedback yet, so I'm re-posting here in the hopes of getting some more exposure. Sorry for the long question. I ...
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21 views

Normalize estimated probabilities from two logistic regression models

I have built two logistic regression models predicting the probability of purchase of two products. (Product A and Product B) For every customers, I want to choose the product that has the higher ...
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16 views

Help Simple Conditional Counts Example

Let's say we have a sequence $S$ \begin{align} t \quad 0 \quad 1 \quad 2 \quad 3 \quad 4 \\ S_t \quad 1 \quad 1 \quad 0 \quad 0 \quad 1 \end{align} And we want to predict $S_{t+1}$ from by ...
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30 views

Confusion about joint and conditional probability

A person has 16 headaches (H) in 30 days, means P(H) = 16/30 = 0.53 The person tracked his Stress Level and Lack of Sleep for those 30 days. It is assumed that High Stress (HS) and Lack of Sleep ...
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1answer
21 views

Order Statistics Conditional Distribution of Affiliated System

We have a system with $M (M\ge 2)$ random variables. The M variables are related as follows. For each i, 1 to M, $X_i = I_i+Z$, where $I_i$, Z are independent uniform random variables. What is the ...
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1answer
76 views

How to calculate joint probability based on result of two conditional probabilities?

I have P(Headache|Stress) = 0.88 where Stress is a "necessary" cause. Again, I have P(Headache|Coffee) = 0.35 where Coffee is also a "necessary" cause. Now I want to calculate joint effect of Stress ...
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27 views

Conditional probability with multiple dependent conditions

A set of items is said to be incorrect if at least one item in the set is incorrect. Initially, all items have equal probability of being correct/incorrect (P = 0.5). A series of infinite events ...
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63 views

Conditional PMF for $P_X(x) = \frac{2(x - a + 1) }{(b-a+1)(b-a+2)}$

The PMF of random variable $X$, is given by: $$P_X(x) = \begin{cases} \frac{2(x - a + 1) }{(b-a+1)(b-a+2)} & a \leq x \leq b \\ 0 &\mathrm{otherwise}. \end{cases}$$ Assume $a < 0$ and ...
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136 views

Conditional Expected Value of Product of Normal and Log Normal Distribution

Could someone please provide the answer and steps to solve this expression? \begin{eqnarray*} & & ...
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32 views

How is free energy an unnormalized conditional log-probability?

I am following Bengio's Learning Deep Architectures for AI and at page 28 there is a phrase that confuses me: $a(x)$ is the discriminant function or an unnormalized conditional log-probability, ...
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14 views

Computing covariance between normal and uniform distributions

I think that this question is related: Covariance of a compound distribution, but it's too abstract for me (I believe that what I have to do must be simpler). Here's the given: machines $A$ and $B$ ...
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55 views

Bayesian Network Problem: What is P(A=T, B=T, C=F, D=F)?

Suppose you have these probabilities in a bayesian network. What is P(A=T, B=T, C=F, D=F)? I attempted to answer this by saying that P(A,B,C,D) = P(A) P(B|A) P(C|A,B) P(D|A,B,C), according to the ...
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1answer
28 views

how to calculate the following conditional probability

There are two events involved, say event A and event B. I want to know the probability of event B conditioned on the event A. The relation between the two events are as follows. We can not talk about ...
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3answers
68 views

Conditioning on vs. fixing a random variable

I am confused by the following notation, seen used by a professor in a course I'm taking. $p(X|Y)$ denotes the conditioning of a distribution over a random variable $X$ by $Y$ and $p(X;y)$ denotes ...
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175 views

Multiple conditional probabilities

Similar questions have been asked in this context but this one seems a bit different. [Aim] We would like to find out what the probability is of a person purchasing a 4USD column D (see below) price ...
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33 views

Example for conditional Poisson regression

I am working with the dataset below, I am trying to predict the chances of ...
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38 views

P(U | C) = ? where U = (A, B) where A and B are independent events

I want to calculate $P(C | A, B)$ or $P(C | U)$. I know $P(C | U) = \frac{P(U | C) \times P(C)}{P(U)}$. Since $A$ and $B$ are independent, $P(U) = P(A)\times P(B)$ But how to calculate $P(U | C)$? ...
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38 views

Evaluating the conditional distribution $f_{Y|X}(y|x)$ without the joint distribution $f_{XY}(x,y)$

Let the distribution $Y = X + N$. Where $X$ and $N$ are independent and they have distinct distributions. I have $f_X(x)$ but I don't have the $f_{XY}(x,y)$ to use, for example, the following ...
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17 views

Calculating empirical distribution function from data

Suppose that we have a matrix (n lines and 3 column) which represents the value of three variable X, Y, Z at some instants : X Y Z x1 y1 z1 x2 y2 z2 ... xn yn zn Given that X ...
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1answer
47 views

Conditional density of bivariate normal and normal

Let $Z=X+Y$ where $X \sim N(\mu,\sigma^2)$ and $Y \sim N(0,1)$ are independents. What is the conditional density of X given Z, $f_{X|Z}(x|z)$? I already found that ...
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7 views

Conditional probablity of k-th order statistic of a column given the k-th order statistic of the sum of the columns?

Suppose A is a random matrix. Each row is a series of i.i.d random variables. I like to know if we can calculate the conditional probability (for a given $k$) $$P\big(A^i_{(k)} \mid (\sum ...
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1answer
77 views

Conditional probability

I have been working on a question for hours now and I thought I would ask stack exchange. "Deer ticks can be carriers of either Lyme disease or human granulocytic ehrlichiosis (HGE). Based on a ...
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197 views

How to understand Gibbs distribution

I have a graph model such as Following the Hammersley–Clifford theorem describes that Markov random fields exhibit a Gibbs distribution with an energy function as follows: $$P(x)=\frac ...
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1answer
30 views

Conditional probability of intersection of multiple hypergeometric distributions

What's given: I have an urn with with a set $S$ of balls where $|S| = N$. Each ball $b_i$ has a unique id and can either be red or blue. There are $m$ red balls in the urn. $d$ times I randomly draw ...
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1answer
35 views

Given $P(X\perp Y\;|\;Z)$ and $P(X\perp Y\;|\;W)$, prove or disprove that $P(X\perp Y\;|\;Z, W)$

Given $P(X\perp Y\;|\;Z)$ and $P(X\perp Y\;|\;W)$, prove or disprove that $P(X\perp Y\;|\;Z, W)$ I'm pretty sure this isn't true, as I haven't been able to prove it using Bayes' Theorem and messing ...
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33 views

How to test the significance of the sum of two conditional probabilities?

I am trying to test whether traders can trade profitably in both long trades (i.e. buying an asset) and short trades (i.e. selling an asset). To do this, some studies (here, see page 464) in finance ...
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1answer
74 views

Can $P(A \cap B)$ be computed as $P(A)*P(B|A)$ and vice versa in any example?

Following Bayes example is taken from here A math teacher gave her class two tests. 25% of the class passed both tests and 42% of the class passed the first test. What percent of those who ...
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14 views

Bayesian posterior with multiple signals and constraining equation/slice

Prior and signals: Let $y_1$ and $y_2$ be iid signals on $Y$. The intial prior is $Y \sim N(\bar{Y}, \sigma^2_Y)$, where $N(\cdot, \cdot)$ is the normal distribution The signals are independent and ...
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1answer
38 views

How do perform conditional ordered logit / probit regression

I am attempting to model the finishing position (independent variable) of runners in a race based upon height, weight, age, gender, past results (dependent variables). Thusfar I have performed an ...
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47 views

Does f(a,b|c) indicate a and b are both conditioned on c, or only b?

Simple question: I know f(a|b,c) indicates a is conditioned on 2 variables b,c however, does f(a,b|c) indicate a and b are conditioned on c, or just b? If this notation means is a conditioned on ...
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48 views

How can I infer the value of multiple dependent continuous random variables in conjunction with discriminative learners?

I have 2 continuous random variables V1, V2 which are dependent. I want to infer each of their values based on: The value of ...
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2answers
42 views

Probability of winning one contract

I have been trying to figure out the following question: A private company has submitted bids on two separate federal government contracts. The company president believes that there is a 45% ...
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21 views

Incorporating background knowledge into a model?

I have built a model that predicts the class of an observation, based on explanatory variables A; i.e. predicting P(y|A). From domain knowledge and academic literature, we know that other variables, ...
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24 views

Conditional independence conjecture

Suppose there are four random variables (events), $A$, $B$, $C$ and $X$. If we have $X\perp A|B$, saying $X$ and $A$ are conditional independent given $B$, then I want to ask that whether we have ...
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1answer
47 views

How to compute $P(|X - E_Y[h(y)]| < c)$?

Consider a discrete random variable $Y$, a continuous random variable $X$, and a constant $c$. The goal is to find $$P(|X - E_Y[h(y)]| < c),$$ when we are only given $P(y)$, function $h(y)$, and ...
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2answers
53 views

How do you calculate a Poisson distribution for matched data?

I am trying to find the rate of infections with 2 different treatments and to see if there is any difference between them. I want to work out whether the rate of 'no infections' is different between ...
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2answers
28 views

How to find conditional distributions from joint

I want to learn about how to do Gibbs sampling, starting with finding conditional distributions given a joint distribution. While looking for examples, I found this blog post that I wanted to ...
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1answer
78 views

Semicolon in probability expression

I run in to this formula when reading a tutorial: $$ \begin{align} P(\pi|\mathbf L;\gamma_{\pi1}, \gamma_{\pi0}) & =P(\mathbf L|\pi)P(\pi|\gamma_{\pi1},\gamma_{\pi0})\tag{28} \\ &\propto ...
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38 views

Why is Bayes theorem more popular than the normal definition of P(A|B)? [duplicate]

As everyone knows, the conditional probability of A given B is $P(A|B) = \frac{P(A\cap B)}{P(B)}$, and Bayes' theorem is derived from that equation to $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$. I'm pretty ...
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14 views

Conditional probability with joint distribution gaussian [duplicate]

Given that $(x_1, x_2)$ are jointly normally distributed with $\mu = 􏰃\begin{bmatrix} \mu_1 \\ \mu_2 \end{bmatrix}$ 􏰄and $\Sigma = \begin{bmatrix} \sigma_1^2 & \sigma_{12} \\ \sigma_{21} & ...
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1answer
52 views

Probability of P(A,B|C)

I just want to double check that this is true. Google doesn't cooperate well with equations. P(A,B|C) = P(A|B,C)P(B|C)
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22 views

Attraction/ likelihood of going somewhere given similar people have already gone

Given a venue which has previously been attended by a demographic of people (e.g. old, young, middle age) I want to compute the affinity those demographics have for a venue and therefore compute the ...
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1answer
65 views

Question about Conditional Probability

I have: P(c) = 0.98 and P(v) = 0.96. Also I have this conditional probability table: ...
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1answer
27 views

What is the predictive distribution of Bayesian supervised Learning? (rigorous argument)

I was trying to understand the posterior predictive distribution for any supervised predictor (by that I mean any classifier or regression predictor $f$). The exact equation I am unsure of is: $$ ...
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1answer
42 views

Is this an instance of the base-rate fallacy?

The following line of probability reasoning is supposedly fallacious, and is an instance of the base-rate fallacy. The argument is that $(1)-(3)$ don't give us enough reason to conclude that $(C)$. ...
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42 views

How to exploit relationships between independent variables?

Data: Each instance (representing a document) is a bag-of-entities (like BOW, except they're Wikipedia entities instead of words), so each feature is a binary or tfidf-like score based upon the ...
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2answers
50 views

Conditional probability of first ball being blue given that the second ball is red

Start with an urn with 5 red and 3 blue balls in it. Draw one ball. Put that ball back in the urn along with another ball of the same color. Now draw another ball from the urn.Suppose the second ball ...
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1answer
22 views

Clarification on Notation

I'm using Andrew Gelman's 3rd edition of Bayesian Data Analysis and am going through the exercises. For one of the exercises, he supposes that if $\theta = 1$, then $y$ has a normal distribution with ...
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2answers
109 views

Distribution and knowledge about a state of the environment

Let's assume I have a frequency distribution for train travel times, estimated based on one month of empirical data: [1:00h, 1:20[ : 20% [1:20h, 1:40h[ : 50% [1:40h, 2:00] : 30% Edit: The data ...