# 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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### Problem with simulate $X$ with $X|Y = y \sim Exp(y)$ and $Y \sim Exp(1.5)$

II'm trying to simulate $X$ with $X|Y = y \sim Exp(y)$ and $Y \sim Exp(1.5)$, I found that $$f_X(x) = \frac{1.5}{(1.5 +x)^2 } , x > 0$$ When I do the simulation, it does not give me good ...
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### How to evaluate this conditional expectation for the E-step in expectation-maximisation?

I'm trying to devise an expectation-maximisation algorithm for a certain problem but I'm unable to derive the conditional expectation in the E-step. For the purpose of this question I'll simplify the ...
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### Applying Bayesian probability to a generalized Monty Hall problem

I posted this question about the Monty Hall problem and Monty's knowledge of the probability distribution several months ago. I got some good answers and this one in particular helped me gain some ...
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### Deriving the log-likelihood function for ACD (Autoregressive Conditional Duration) models

I am trying to understand the procedure that is shown in this survey to obtain the log-likelihood function to estimate the parameters for an ACD model: PACURAR, Maria. Autoregressive conditional ...
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### Gambler ruin's: Probability of k consecutive win before j consecutive loss

Assume that a stock has a probability of $p$ to win, a probability of $q$ to lose, and a probability of $(1-p-q)$ to remain every day. What is the probability of $k$ consecutive wins occur before $j$ ...
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### Transformer model conditional probability distribution of sub-sentences

I have a simple transformer model (decoder only) which is trained on some dataset containing sentences to do next-word prediction. The model captures a probability distribution $P_{\theta}(\mathbf{a})$...
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### Conditional probability exercise: is this the right way?

I have a Pandas DataFrame and I have to calculate a particular probability. I don't have problems with the code, but with the mathematical concepts I have to use. The DataFrame contains information ...
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### About the use of Bayes' rule for continuous valued random variables

I am currently studying the book "An introduction to statistical learning with application in Python" and I am currently at the part 4 of chapter 4 where they explain the general framework ...
1 vote
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### How to handle "multiple" conditional probability like P(A|B|C)? [closed]

We know that P(A|B)=P(A,B)/P(B) but what if we want to find the analog for this "multiple" conditioning P(A|B|C)?
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### How to obtain $p(x)$ given samples from $p(y|x)$ and $p(y)$?

Here, assume both $p(y\mid x)$ and $p(y)$ are too complicated to get closed forms, and we can only draw samples from them. Is there any way to estimate or draw samples from $p(x)$?
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### Looking for terminology to describe a certain partial independence condition on conditional probability

I find myself in a position where for events $X,Y$ and $Z$, I might have $$P(X|Y,Z) = P(X|Y)P(X|Z)$$ I don't know what to call this, and it's difficult to search for potential phrases, since all ...
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### Borel-Cantelli lemma on conditional probabilities

In a probability space $\big( \Omega, \mathcal{F}, P \big)$, suppose $\{E_n\}_{n\in \mathbb{N}} \subseteq \mathcal{F}$ is a sequence of mutually independent events. By Borel-Cantelli Lemma, the ...
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### Do Bayesian networks have any rules with regards to zero probability RVs?

I am currently learning about Bayesian networks through Berkeley's AI course. In a Bayesian network, each node encodes the conditional probability of the random variable (RV) represented by the node ...
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### How to derive conditional posterior predictive distribution from definition of posterior predictive distribution in bayesian regression?

In my situation, I have a set of data points: $$z_{0:n} = \\{ (x_0, y_0),\dots ,(x_{n-1}, y_{n-1}) \\}$$ I am trying to figure out how to derive the fully expanded form for the conditional posterior ...
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