# Questions tagged [conditional-probability]

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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### Understanding conditional notation

Which is the correct way to describe the conditional probability distribution of X conditioned upon Y where X = a, Y = b $$P_{X \mid Y}(a \mid b) \tag1$$ or $$P_{X \mid Y}(a,b) \tag2$$ What is the ...
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### What is the exact role of model $p_\theta$ in Diffusion models for the reverse process?

I'm reading this interesting blog post explaining Diffusion probabilistic models and trying to understand the following. In order to compute the reverse process, we need to consider the posterior ...
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### How can we expand the following probability?

Suppose we have a predictive regression of the form \begin{align} y_t=\beta x_{t-1}+u_t\\ x_t=\rho x_{t-1}+\varepsilon_t, \end{align} for $t=1,\cdots,T$, such that $cov(x_{t-1},u_t)=0$ for all $t$, ...
1 vote
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### Given all conditional probabilities, find joint probability

For two random variables $A$ and $B$, if we know $\mathbb{P}(A|B)$ for all possible values of $A$ given all possible values of $B$ respectively, and $\mathbb{P}(B|A)$ for all possible values of $B$ ...
1 vote
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### Intuition about the relation between joint distribution, marginal distribution, and conditional distribution

The wording "intuition" might be a bit imprecise. I want to discuss how we visualize in our head going from one to another among the joint PDF, marginal PDF, and conditional PDF. To make the ...
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### Finding the conditional distribution from given normal distributions using Bayes' theorem

Background This question is related to my previous question: Describing the measurement of a random variable as another random variable, but I've narrowed and clarified my question. I think I've ...
47 views
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### calculate combination of matrix of probabilities (win rate ranking in game)

Let imagine we have a game with 4 players. And after playing game, we will get ranking of 4 players based on their score, rank 1 is the best, rank 4 is the worst. I have created a model for predicting ...
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### Describing the measurement of a random variable as another random variable

Background Suppose we have a box of resistors. The manufacturer rates these resistors at 100 ohms, but they have some variability. Let $x$ be the true resistance of a resistor chosen from the box at ...
499 views

### is P(notB|A) same as not(P(B|A)) [closed]

is P(notB|A) same as not(P(B|A)) if not then what is the difference between them? this is taken from bayes question.
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1 vote
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### Product of kernels vs Composition of kernels

According to Wikipedia there are two main operations between two kernels: product and composition. They look almost identical to me and I cannot figure out what's the intuition between these different ...
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### What's the conditional variance of the chain X -> Y -> Z?

If I have a cascade of 3 random variables, represented as a Bayesian Graph: $X\rightarrow Y \rightarrow Z$, is there a simple formula for $\sigma_{X|Z}$? Further, assume all the variables are normal, ...
1 vote
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### How to calculate conditional probability on student multivariate distribution

I have a multivariate student distribution fitted on some data on 4 dimensions (so I know the parameters). I am trying to calculate the $P(X_4\le x_4| X_1=x_1, X_2=x_2, X_3=x_3)$ but falling short. I ...
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### Estimate distribution of variable from non-perfect predictions

Say I pull $n$ balls from a box while blinfolded. The balls can be either red or blue. I do not know the distribution of the balls. After that I receive a list predicting the color of every ball I ...
1 vote
87 views

### On the likelihood assessment of two extremely rare events

I've been pondering the concept of subjectivity to evaluate likelihood and predictability of extremely rare events. I'd like to demonstrate my question over trivial hypothetical examples below. I did ...
1 vote
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### A variation of boy-or-girl paradox

I was working on this problem but the extra information supplied seems so superfluous and I'm trying to figure out if it is meaningful, and how it is meaningful. Given: This video has presented two ...
### Does the density $g(y) \propto (1-y^2)^{(n-3)/2} e^{\delta y} \quad\text{for}\quad |y| \leqslant 1$ have a name?
The following probability density function has a particularly simple form, and it was produced when deriving a confidence interval for $\frac{\mu}{\sigma^2}$ , g(y;\delta)=c_\delta(1-y^2)^{(n-3)/2}e^...
Suppose A and B are two propositions and $A \implies B$ is true.WE know all it means is that B is true whenever A is true. Now consider a situation where we only that A is true with probability ,say,...