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).

learn more… | top users | synonyms

1
vote
0answers
7 views

Help interpreting this result based on conditioning on gender -Contigency Tables

The problem i'm having is how to interpret the results I got. For part a) I got that the abortion laws are independent of generation where I used a $\chi^2$ test. For part b) I got that the the age ...
0
votes
0answers
10 views

How to test a probabilistic fertility simulation?

Imagine I want to build a simulation of a certain society. One part of it is a fertility model, which describes under which circumstances people are born. Let's assume that the model is very simple: ...
0
votes
0answers
17 views

Variance of multinomial distribution that is product of 4 Beta random variables

I have a system of 4 binary random variables, $A$, $B$, $C$ and $D$. $A$, $B$ and $C$ are conditionally independent given $D$, and I'll call one set of samples $ABCD$ an event (e.g. $ABCD$ meaning all ...
0
votes
0answers
8 views

scikit learn gaussian mixture conditional distribution

I am using scikit-learn to fit a Gaussian Mixture Model to a dataset. However, I now need to find the distribution conditional on one or more variables and I have not found a way to do that. Can ...
1
vote
0answers
46 views

An 'easy' exercise on conditional expectations and filtrations

I am struggling with the following exercise in the context of modeling information structure via filtration to evaluate contingent claims. I hope that someone can explain me how to derive the ...
1
vote
0answers
27 views

Marginal, joint, and conditional distributions of a multivariate normal

Let $Y$ ~ $MVN_3(\mu, \Sigma)$ where $\mu = (5,6,7)$ and $\Sigma = \begin{bmatrix}2 & 0 & 1\\0 & 3 & 2\\1&2&4\end{bmatrix}$ Find (a) The marginal distribution of $Y_1$ (b) The ...
-1
votes
0answers
18 views

On conditional/joint probability [duplicate]

Problem 1 The table on the left shows the joint probability distribution between two random variables - X and Y; and the table on the right shows the joint probability distribution between two random ...
0
votes
0answers
6 views

Dependence of PDF of LLR of symbols

I have a system model with $y=hs+\sum_i^n gx+n$ where h is rayleigh fading desired channel, g is interfering channel x is interfering symbols. $\hat{s}=w*y$ where w is MMSE filter. On what factor pdf ...
1
vote
0answers
19 views

conditional distribution question

I have a joint distribution which factorizes as follows: $$ P(y, w, \beta) = P(y|\beta, w) P(w) P(\beta) $$ Now, I want to write the conditional distribution for $P(w|y, \beta)$, so this should be ...
0
votes
0answers
23 views

t-student distribution [duplicate]

I've got this problem: Here, if $Z,W$ are independent random variables, and $Z$ has normal standart distribution and $W$ has $\chi^2$ with $n$ degrees of freedom, $T=\frac{Z}{\sqrt{\frac{W}{n}}}$. I ...
0
votes
1answer
23 views

conditional probability, change of variable and Jacobean

I have a question, and I am guessing that the question arises due to my lack of good understanding in the change of variable technique. I would like to evaluate $f_X(x)$. When $f_Y(y)$ exists, I can ...
1
vote
0answers
10 views

Estimating conditional probability of bernoulli data

Assume I have $i=1,\dots,N$ fathers, each with $j=1,\dots,n_i>0$ sons. Now there is a binary event $A_{i,j}$ with outcomes 1 and 0 and the respective probabilities $p$ and $1-p$. Now I want to ...
2
votes
1answer
40 views

On an implication of the memoryless property of the exponential random variable

I know that if we take $X \sim Exp(k)$ then we have this property: $$P(X \ge s + t | X \ge s) = P(X \ge t)$$ But why does this imply that $X | X > x$ has the same distribution of $X$ only ...
0
votes
1answer
15 views

Posterior probability of an image when the posterior of local features are known

Lets assume the local features $x_1, x_2, \dots x_n$ of an image $I$ are independent. I know if $p(x_i|c)$ are given $p(I|c)$ can be defined by $\prod_{i=1}^N x_i$ But I dont know how to calculate ...
0
votes
0answers
30 views

A question about raising the power of the integrand

Given that we know $P(X<x)=F(x)=\int_{\theta}F(x|\theta)dG(\theta)=1-\alpha$, is there any way to express $\int_{\theta}[F(x|\theta)]^{n}dG(\theta)$ also in terms of $\alpha$?
0
votes
0answers
34 views

Is is possible to determine conditional conjugacy in this case?

I'm working on a problem where I have to extract sufficient statistics for parameter estimation in a state-space model. Usually these come from the quantities used for conjugate updates. I'm OK with a ...
5
votes
2answers
144 views

A Question on Elementary Statistical Inference

A box contains $5$ white and $2$ black balls. A coin with unknown $P(Head)=p$ is tossed once. If it lands HEADS then a white ball is added, else a black ball is added to the box. Then a ball is ...
0
votes
1answer
38 views

What does “if” mean in this question?

What is the probability that Sam is guilty if Tom and Devi gave conflicting testimonies? Is it conditional probability? Or intersection simply?
0
votes
0answers
13 views

Alternative answer to choose k people out of n, then choose 1? [migrated]

The question is fairly simple, we first choose k people out of n, that is $C(k,n)$ as the combination function, then we choose 1 person out of k, we have k choices. The total number of choice is given ...
1
vote
1answer
44 views

Sufficient statistic for a Gamma distribution

I am confused about the steps I need in order to solve the equation below. I must use conditional distribution (and NOT the factorization theorem). Q: $X_1, . . . , X_n$ is a random sample from a ...
0
votes
0answers
37 views

Bayes Net: how to calculate joint distribution?

I originally posted this question to Computer Science Stack Exchange, but then I was told that CrossValidated site existed. I've been reading many questions, but none of them seem to answer my doubts. ...
1
vote
0answers
26 views

conditional density wrt lebesgue measure

$X,Y$ are two r.v. $(\Omega,\mathcal{A},\mathbb{P}) \rightarrow (\mathbb{R},\mathcal{B}(\mathbb{R}))$ and have joint density wrt to $\lambda^2$, the two dimensional lebesgue measure. So $f_X(x) = ...
0
votes
0answers
31 views

Conditional distribution function of sum of correlated Bernoulli variables

Let $X_i$ be a Bernoulli variable with probability $p$ for $i=1,...,N$. Hence $\sum_i X_i$ is binomial and approximately normal$(p,(1-p)p/n)$ for large $N$ The conditional probability distribution of ...
0
votes
0answers
17 views

Conditional distribution of current state of HMM given past observations and state

I want to compute the following conditional probabilities for an HMM, where I shall refer to the state at time $t$ as $X_t$ and the observation at time $t$ is $O_t$: $$\text{Pr}\left(X_t | O_1, ...
0
votes
0answers
37 views

Conditional probability attributes

Let $(\Omega,\mathcal{A},\mathbb{P})$ a probability space and $\mathcal{F} \subset \mathcal{A}$. For $B \in \mathcal{A}$ is $\mathbb{P}(B|\mathcal{F}):= \mathbb{E}[I_B | \mathcal{F}]$ the conditional ...
0
votes
0answers
16 views

Dealing with independent events and a “given” statement

I'm given a question: Two buddies, plan a squirrel-hunting trip. B has a shot 2x better than A. A's chance of hitting the squirrel is 0.39, they see a squirrel and both shoot at the same time. ...
1
vote
0answers
41 views

Probability problem (Urn 1 contains 3 white and 4 black balls, and Urn 2 contains 2 white and 6 black balls …)

I'm studying probability. This is not homework. I have been studying for a graduate master's since September 2015. The textbook is Probability : An Introduction (Grimmett & Welsh). You are ...
4
votes
1answer
74 views

Gibbs Sampler transition kernel

Let $\pi$ be the target distribution on $(\mathbb{R}^d,\mathcal{B}(\mathbb{R^d}))$ which is absolutely continuously wrt to the $d$-dimensional Lebesgue measure, i.e : $\pi$ admits a density ...
7
votes
2answers
150 views

Conditional probability of continuous variable

Suppose that random variable $U$ follows a continuous Uniform distribution with parameters 0 and 10 (i.e. $U \sim \rm{U}(0,10)$ ) Now let's denote A the event that $U$ = 5 and B the event that ...
5
votes
1answer
164 views

Gibbs Sampler contradiction proof

I want to prove that the systematic scan Gibbs sampler yields an aperiodic chain $X$ on a general state space. Let $\pi$ be the stationary distribution for the resulting chain. Suppose to get a ...
1
vote
1answer
45 views

Conditional distribution for Exponential family

We have a random variable $X$ that belongs to the exponential family with p.d.f. $$ P_X(x|\boldsymbol \theta) = h(x) \exp\left(\eta({\boldsymbol \theta}) . T(x) - A({\boldsymbol \theta}) \right) $$ ...
1
vote
0answers
61 views

Using inverse probability with conditional events

To reach Grenoble, France, from Turin, Italy, one can follow either of two routes. The first directly connects Turin and Grenoble, whereas the second passes through Chambery,France. During extreme ...
0
votes
0answers
17 views

joint distribution translated into union of intersection?

Consider the declaration of the intersection property for conditional independence. $$ \left.\begin{align} X \perp\!\!\!\perp A \mid B \\ X \perp\!\!\!\perp B \mid A \end{align}\right\}\text{ and ...
1
vote
1answer
95 views

Conditional Probability [duplicate]

A judge is 35% sure that X has committed a crime. A and B are two witnesses who know whether X is innocent or guilty. However, A is X’s friend and will lie with probability 0.25 if X is guilty. He ...
0
votes
1answer
22 views

Selecting the best subset of features in binary logistic regression [duplicate]

I am using a binary logistic regression (a type of probabilistic statistical classification model, is used to predict a likelihood of belonging to a class (True, False)). I have 4 features and I want ...
1
vote
1answer
40 views

Conditional probability density function

Let $\theta$ be the parameter of the probability density function $f(x)$. If it is mentioned that $f(x|\theta)$ be the conditional probability density function, then what does $f(x|\theta)$ mean? ...
0
votes
0answers
18 views

Finding conditional probability on movement of knight

A knight makes 10 random moves on a chessboard, starting from bottom left hand corner. Let $A_k$={no square is repeated within the first $k$ moves} Find $P(A_{10}|A_5)$
-1
votes
0answers
18 views

Conditional Density Formula (using Gaussian copula)

Is it true that $R_k$ can be calculated using Pearson correlation, Spearman's $\rho$ or Kendall’s $\tau$? And is it true that If we use Pearson correlation, then the correlation(covariance) $R_k$ in ...
0
votes
0answers
22 views

Closed form Pocock Rejection Region solution for joint MVN correlated RVs?

This is related to my previous question (link), but I have a simpler way of expressing it. Suppose $ \left( \begin{array}{ccc} \ Z_1 \\ Z_2 \end{array} \right)$ follows a Bivariate standard normal ...
4
votes
1answer
54 views

How to derive the conjugate prior of an exponential family distribution

I am trying to derive the conjugate prior of the univariate Gaussian distribution over both the mean and the precision. I know that the prior I'm looking for is the normal-gamma distribution, but the ...
0
votes
0answers
17 views

A Conditional Probability Question

Assume we know $$p(w) \sim N(0, \Sigma)$$ $$p(e) \sim N(0, 0.01)$$ $$y=w^\intercal x$$ $$o = y + e$$ Where w/x/o/y/e are all vector How do we calculate the distribution of $$p(y|o,x)$$
1
vote
1answer
55 views

Specify conditional probability of a continuous node given a continuous node as its parent

This question is essentially same as this one. The question is: How do you calculate conditional probability of a node in Bayesian network when it has a continuous node as a parent? However, I cannot ...
0
votes
1answer
63 views

Why can we assume that samples $X_i$'s are independent if the parameter is fixed (though unknown)?

To put it in context, I was trying to learn Bayesian parameter estimation (by an example of learning the probability of heads of a coin) and was trying to understand the independence of the samples ...
0
votes
1answer
26 views

How to estimate rating of a customer?

I have data about customers transactions contains: ratings of customer $r_{ci}$ to service $s_m$ which has quality $q_m$. Quality is assumed to be a real value from [0, 1]. Rating is discrete values ...
0
votes
0answers
16 views

Conditional Probability in Multivariate Normal

Given a tri-variate Normal, the conditional probability of an element given others truncated information is Now if I know that the mean vector u is (-0.91,-1.31,-1.39) and R is ...
0
votes
0answers
20 views

conditional probability in correlated variables

I tried to generate random samples to provide some scenarios for a stochastic programming model. I have three correlated stochastic variables. It is needed to calculate probability of each sample ...
0
votes
1answer
35 views

Does martingale model work for betting football matches?

Imagine I have 1 million USD and will be betting 1.000 USD on the win of FC Barcelona each time they play a match in La Liga (Spanish Tier 1 football league). If FC Barcelona loses or ties their last ...
1
vote
0answers
12 views

Describing a distribution of probabilities/percentages

Is there a better way to describe this probability? \begin{equation} Pr(Y_{sij}|R_n) = \frac{Y_{sij|R_n} \sum_{ij}Y_{sij}}{\sum_{ij|R_n} Y_{ij}\sum_{sij}Y_{sij}} \end{equation} The $R_n$ describes ...
0
votes
1answer
50 views

Graphical dependence in the DAG X->Z<-Y

In Barber's book pp. 40-41 he says that the belief network X->Z<-Y: is "graphically dependent" since: $$p(x,y|z) \propto p(z|x,y)p(x)p(y)$$ I don't understand why graphical dependence follows ...
2
votes
1answer
30 views

Can I rewrite conditional probability of three variables like this?

I know that the conditional probability $p(x\mid y)$ is defined as $\frac{p(x,y)}{p(y)}$. But what if I have $p(x,y \mid z)$, is that the same as $\frac{p(x,y,z)}{p(z)}$?