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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Joint PDF of ordered statistics [on hold]

Let $Y_1 < Y_2 < … < Y_n$ be the order statistics of $n$ independent observations from a continuous distribution with cumulative distribution function $F(x)$ and probability density ...
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1answer
23 views

Conditional expectation for non-gaussian variables

Let $A$, $B$ be two zero-mean random variables. Let the variance be $\sigma^2_A$, $\sigma^2_B$ and let the correlation be $\sigma_{AB}$. Consider the following expression :- $$ ...
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10 views

Conditional Distribution of Hidden Markov Model

I am trying to implement a Gibbs sampling algorithm for a toy Hidden Markov Model, but I am having trouble deriving the target conditional distribution. I am generating data through the following ...
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2answers
79 views

Is it correct? $ p(a,c|b) = p(a|c)p(c|b) $

I read two different papers on some similar problems. In one of the papers this statement is written: $ p(a|b) = \sum_{c \in C}p(a,c|b) $ While in the other it is written as: $ p(a|b) = \sum_{c \in ...
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1answer
34 views

How to do calculate both causal and diagnostic inferences simultaneosly in bayesian networks?

Consider a simple Bayesian network as given below. Question: How to find $P(S|C,W)$? It is fairly straight forward to compute the causal inference $ P(W|S) = P(W|S,R)\cdot P(R) + ...
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44 views

If the # of people in a room is Poisson distributed, and you observe someone enter, what's the distribution of the # of people?

I hope this question is properly formulated. It's just something that occurred to me spontaneously. Consider a random variable $X$ representing some count data -- for instance, the number of people ...
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0answers
15 views

posterior distribution for coin flips given uniform prior distribution [closed]

A coin has an unknown head probability $p$. Flip $n$ times, and observe $X=k$ heads. Assuming an uniform prior for $p$, then the posterior distribution of $p$ is the beta distribution $B(\alpha = k + ...
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1answer
90 views

Probability distribution transformation of variables question

Problem: Hi there, I'm stuck trying to derive an equation stated in a research paper relating to Bayesian statistics in Cosmology (the paper is: ...
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1answer
54 views
+50

Estimating a function $f$ of a random vector $\mathbf{x}$ by a subset of the coordinates of $\mathbf{x}$ after a rotation of the input space

Suppose I have $$h=f(\mathbf{x})$$ with $f$ a deterministic function and $\mathbf{x}=(x_1,\ldots,x_n)$ a random vector of known distribution. I'm not using the capital letter notation for random ...
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0answers
9 views

Sample space in Linear regression

Say you want to model some trait of an individual using standard linear regression. Then you assume $Y|X\sim N(\boldsymbol{X}\beta,\sigma^2)$, where $\boldsymbol{X}=(X_1,...,X_n)$ is a row-vector of ...
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35 views

A question on conditional gaussian distribution

The book on Pattern Recognition (by Bishop) begins the section on conditional gaussian by saying: An important property of the multivariate Gaussian distribution is that if two sets of variables ...
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1answer
10 views

Conditional probability sub-model so solve setting with a factor that has many levels

I stumbled upon a post of the http://www.win-vector.com/ blog where they treat the problem when a factor with many levels occurs. In my understanding instead of using the factor itself, they use the ...
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0answers
31 views

how do i compute the probability [duplicate]

I have a continous dataset consisting of 4000 observation from each 400 features are extracted. Each observation has been labeled a class. Since the dataset is continous, have I created a distribution ...
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1answer
33 views

When is the probability of a variable equivalent to a function of the variable i.e. when does p(x)=f(x)?

What allows us to conclude that that p(z)= h(z) as shown in the yellow highlights in the below solution? If p(z) didn't equal h(z) then proportionality would still fail to show conditional ...
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2answers
50 views

P(X<Y|Z=t) where Z=min(X,Y)

Lets X and Y be uniform random variable where $x \in [0,a]$ and $y \in [0,b]$ where a < b. We design $Z=\min(X,Y)$. I know that the CDF of Z is $P(Z<z)=1-\frac{(a-z)(b-z)}{ab}$ And by ...
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1answer
30 views

Bayesian networks - prediction question

Let's consider a dumb spam filter BN (see figure below) for which I've already calculated the a posteriori parameter distributions (see normalized table values). I want to predict if next email ...
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1answer
58 views

Joint distribution of a discrete and a continous random variable

Consider this question and the working below: A coin-making machine produces pennies. Each penny is manufactured to have a probability $P$ of turning up heads. However, the machine draws P ...
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0answers
14 views

Hidden Markov Model with sequence of 1

I'm not experienced with HMM. I read some research papers about HMM and they mention 3 basic problems. One of them is to find the probability of a sequence of $k$ emitted symbols $(S = x_1, x_2,..., ...
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2answers
54 views

Probability Question - Conditional Probability Quantity

A particular fault occurs in a certain type of mechanical devices with a frequency of 8 in 1,000. A screening test for this fault is developed such that (i) if the fault is present, it is detected ...
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2answers
235 views

How to derive this conditional distribution function for a Restricted Boltzmann Machine?

I am following along Ian Goodfellow's new Deep Learning book and, reading the last chapter, I am confused about equations 20.7-20.9. We have a joint distribution function, $P(v,h)$, and we are ...
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3answers
111 views

Bounds on a conditional probability

My friend asked me about this, and I couldn't give him a good answer. Say you have some favorable event $G$. You know that knowing either of events $A$ or $B$ will more likely than not result in $G$. ...
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0answers
15 views

Question about conditional probability for the multivariate normal distribution

How can I prove that the conditional probability of a multivariate normal distribution Pr(x1|x2=k) is the same for all k when the covariance is diagonal and the variables are independent ? Would the ...
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0answers
41 views

Expanding Joint probability distribution function having dependent random variables

Let $Z_1$ and $Z_2$ denotes two dependent random variables defined as \begin{align} Z_1&=\frac{XY}{aX+bY+c}\\ Z_2&=\frac{XY}{uX+vY+w} \end{align} where $X$ and $Y$ are independent ...
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0answers
22 views

Conditional cumulative probability

Given two jointly distributed random variables $X, Y$, I would like to compute the conditional cumulative (or cumulative conditional?) probability $P(X \leq x | y)$ that given a value $y$ of $Y$, $X$ ...
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6 views

Adding dependent random normal distributions and conditional expectations

My problem is as follows: Let $X, B_1, B_2, B_3$ be independent normal random variables with $\mu = 0$, $\sigma = 1$. Let: $Y_1 = X + B_1$ $Y_2 = 2X + B_2$ $Z = X + B_3$ Then, I had to find $Z' = ...
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1answer
27 views

Does Naive Bayes( library:klar) in R calculates denominator of conditional probability while giving output?

Generally, when using Naive Bayes for classification, denominator is ignored as probability is directly proportional to the numerator as denominator is same for all the classes. So, I want to know if ...
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1answer
34 views

Comparing the distribution fits of a bivariate and a univariate model

Suppose I've done an experiment and I have a distribution of observations $x$ that vary between $-\pi$ and $\pi$. Now suppose each $x$ is associated with a second observation $y$ that may or may not ...
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1answer
76 views

Finding Probability Mass Function (PMF) Given a Geometrically Distributed Random Variable and a Negative Binomial Random Variable?

I am a non-student working through the first edition of Yates and Goodman's text, Probability and Stochastic Processes. On page 115, question 3.6.9 goes like this: Each millisecond at a telephone ...
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0answers
19 views

How can I model a process which follows a pdf that changes w.r.t time?

I'm interested in modeling the probability of a gym having had k number of arrivals at time = t. Clearly this should be modeled by some type of time cont. stochastic process but a poisson process will ...
3
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1answer
32 views

Probability explanation for this question

I am just starting to study probability theory, this question may sound naive but I would like to have some qualitative explanation for the below problem. There are 7 balls in a bag. Two balls are ...
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1answer
28 views

Law of total covariance for products of random variables

I have two sets of random variables. $X_i \sim N( \theta, \sigma^2 )$, where $X_i$ are i.i.d. $Z_j$ which are simply iid binary random variables with success probability $p$. I want to find ...
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0answers
9 views

Chi-squared test between a set and its subset

I have a set A and I know that 10% of people in the sample visited a www.site-A.com. Now I extract a sample B, subset of A, of people that have visited www.site-B.com and I assess that 12% of people ...
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0answers
21 views

How to calculate the probability of having n returns in the next 2 weeks?

I am trying to calculate the probability of one product being returned n times in a time window. The Data I only have 1 product I have the time of each sales I have the time of the return for each ...
2
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2answers
115 views

Conditional Probability- hard

Hi guys can someone please help me with the following question: I have come up with the following: a. P(\$20) = (2/3) b. Since Tom states that Jenny used a $10 note we have to assume he didnt ...
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6 views

Inferring previous state in noninvertible continuous state discrete time Markov chain

I've a doubt on how to properly to calculate the backward conditional probability for a subclass of linear systems. Let $x \sim N(0,X)$ and $y \sim N(0,Y)$ be independent variables and $z = A x + y$ ...
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0answers
31 views

How to quantify if one animal is following another

I have information on the order of arrivals of 2 species to food. But I want to find out if species 2 is following species 1. In some cases one of, or neither species will arrive to the food. Would a ...
6
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1answer
93 views

Mars attack (probability to destroy $n$ spaceships with $k \cdot n$ missiles)

Suppose Earth has been attacked by $n$ Martian spaceships and suppose that we have $m=k \cdot n$ missiles to release against the $n$ spaceships. The probability to hit and destroy each spaceship by ...
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0answers
7 views

Genotype of siblings given IBD status (identity by descent status which can be $0, 1,$ or $2$)

I have a question regarding genotype of sibilings (specifically I am referring to the table on slide 19 here: http://ibgwww.colorado.edu/workshop2005/cdrom/ScriptsA/evans/IBDestimation/IBD--2005.pdf ...
3
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1answer
64 views

Estimating P(C|A,B) from P(C|A) and P(C|B): Bayes Rule? Bayes Net? Classifier?

Doing some ecommerce analytics, I want to understand click propensity broken out by different features present in users' profiles. In this scenario, it's easy to test click propensity $p(C)$ broken ...
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0answers
35 views

“probability of a probability”: confusion with categorical and real-value random variables

I think I'm having a "probability of a probability" issue but I don't know how to resolve it: Let's say a variable $l_0$ can take values ${A,B,C}$. I have $N$ training samples $i$ from two different ...
4
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1answer
33 views

Conditional Independence in Graph

I have a factor graph like following: How can I check if Q1 and Q2 are independent given the value of g1? More specifically can someone explain following in easy way? It would be great if you can ...
0
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1answer
28 views

The seemingly backward est. of confidence intervals in Winstein's example

My question is related to Winstein's explanation of the difference between confidence intervals and credible intervals. Please pardon my (at best) amateur rambling, but this has stumped me thoroughly ...
2
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2answers
33 views

How to estimate biases from coin and dice using only observed dice throws in this setup?

To help me understand some concepts I'm learning in my first exposition to machine learning, I'm trying to tackle the following "simple" problem The setup of the problem is as follows: My friend ...
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5answers
338 views

The Frog Riddle - Conditional Probabilities

I saw this riddle doing the rounds on the internet: https://ed.ted.com/lessons/can-you-solve-the-frog-riddle-derek-abbott In summary; There is a population of frogs with male:female occurring in ...
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1answer
19 views

Problem using continuous bayes theorem on multivariate normal distribution

Given three correlated normally distributed variables $ x$, $ y$ and $z$ such that: $ p\left(\begin{bmatrix} x \\ y\\ z\end{bmatrix}\right) \sim \mathcal{N}\left(\begin{bmatrix} 0 \\ 0\\ ...
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1answer
34 views

Doubt on conditional probability of correlated normal variables

I have a system of the form $ \begin{bmatrix} x \\ y\\ z\end{bmatrix} \text{~} \mathcal{N}\left(\begin{bmatrix} 0 \\ 0\\ 0\end{bmatrix}, \begin{bmatrix} \Sigma_{xx} & 0 & \Sigma_{xz} \\ 0 ...
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0answers
22 views

Methodology to generate conditionally independent data correct?

I am trying to generate samples from continuous distributions that are conditionally independent. More specifically, I would like to generate samples from the following joint distribution $f(x,y,z)$ ...
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1answer
18 views

Simple cross-tabulated data and probability

I saw this question which I found confusing: Suppose 400 people are surveyed. For each person, they flip a coin and if it lands heads they are asked, A: Are you a student? otherwise they are ...
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0answers
39 views

Calculating Conditional Probability in Real Data

I have my data in the form as: ...
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13 views

reverse coding before Exploratory Factor Analysis?

Should i do the reverse coding before performing the Exploratory Factor Analysis even though my questionnaires are in positive sentences?