# 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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### Can anyone explain conjugate priors in simplest possible terms?

I have been trying to understand the idea of conjugate priors in Bayesian statistics for a while but I simply don't get it. Can anyone explain the idea in the simplest possible terms, perhaps using ...
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### What is the probability that this person is female?

There is a person behind a curtain - I do not know whether the person is female or male. I know the person has long hair, and that 90% of all people with long hair are female I know the person has a ...
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### Wikipedia entry on likelihood seems ambiguous

I have a simple question regarding "conditional probability" and "Likelihood". (I have already surveyed this question here but to no avail.) It starts from the Wikipedia page on likelihood. They say ...
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### Intuition for Conditional Expectation of $\sigma$-algebra

Let $(\Omega,\mathscr{F},\mu)$ be a probability space, given a random variable $\xi:\Omega \to \mathbb{R}$ and a $\sigma$-algebra $\mathscr{G}\subseteq \mathscr{F}$ we can construct a new random ...
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### Two dice rolls - same number in sequence

I am currently studying Statistical Inference class on Coursera. In one of the assignments, the following question comes up. ...
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### Why Normalizing Factor is Required in Bayes Theorem?

Bayes theorem goes $$P(\textrm{model}|\textrm{data}) = \frac{P(\textrm{model}) \times P(\textrm{data}|\textrm{model})}{P(\textrm{data})}$$ This is all fine. But, I've read somewhere: Basically, ...
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### Problem with proof of Conditional expectation as best predictor

I have an issue with the proof of $E(Y|X) \in \arg \min_{g(X)} E\Big[\big(Y - g(X)\big)^2\Big]$ which very likely reveal a deeper misunderstanding of expectations and conditional expectations. The ...
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### Definition of Conditional Probability with multiple conditions

Specifically, say I have two events, A and B, and some distribution parameters $\theta$, and I'd like to look at $P(A | B,\theta)$. So, the simplest definition of conditional probability is, given ...
• 261
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### Is there any difference between Frequentist and Bayesian on the definition of Likelihood?

Some sources say likelihood function is not conditional probability, some say it is. This is very confusing to me. According to most sources I have seen, the likelihood of a distribution with ...
• 2,069
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### Monty Hall Problem with a Fallible Monty

Monty had perfect knowledge of whether the Door had a goat behind it (or was empty). This fact allows Player to Double his success rate over time by switching “guesses” to the other Door. What if ...
• 339
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### The paradox of i.i.d. data (at least for me)

As far as my aggregate (and scarce) knowledge on statistics permits, I understood that if $X_1, X_2,..., X_n$ are i.i.d. random variables, then as the term implies they are independent and identically ...
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### Why is P(A,B|C)/P(B|C) = P(A|B,C)?

I understand $P(A\cap B)/P(B) = P(A|B)$. The conditional is the intersection of A and B divided by the whole area of B. But why is $P(A\cap B|C)/P(B|C) = P(A|B \cap C)$? Can you give some intuition?...
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### difference between conditional probability and bayes rule

I know the Bayes rule is derived from the conditional probability. But intuitively, what is the difference? The equation looks the same to me. The nominator is the joint probability and the ...
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### A meeting has 12 employees. Given that 8 of the employees are female, what is the probability that all employees are female? [closed]

If I use Bayes' theorem here , event A denoting that 12 employees are female and event B denoting that 8 employees are female, (assuming that an employee has equal chances of being a male or female) I ...
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### How can I calculate the conditional probability of several events?

Could you inform me please, how can I calculate conditioned probability of several events? for example: P (A | B, C, D) - ? I know, that: P (A | B) = P (A $\cap$ B) / P (B) But, unfortunately, I ...
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• 195
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### If $X_1,\cdots,X_n \sim \mathcal{N}(\mu, 1)$ are IID, then compute $\mathbb{E}\left( X_1 \mid T \right)$, where $T = \sum_i X_i$

Question If $X_1,\cdots,X_n \sim \mathcal{N}(\mu, 1)$ are IID, then compute $\mathbb{E}\left( X_1 \mid T \right)$, where $T = \sum_i X_i$. Attempt: Please check if the below is correct. Let ...
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### The more important statistic: '90 percent of all women survived' or '90 percent of all those who survived were women'?

Consider the following statements w.r.t the Titanic: Assumption 1: Only men and women were on the ship Assumption 2: There were a large number of men as well as women Statement 1: 90 percent of all ...
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• 2,501
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### What is "Likelihood Principle"?

While I was studying "Bayesian Inference", I happen to encounter the term, "Likelihood Principle" but I don't really get the meaning of it. I assume it is connected to "...
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### Expected number I will be on after drawing cards until I get an ace, 2, 3, and so forth

I am having some trouble solving the following. You draw cards from a standard 52-card deck without replacement until you get an ace. You draw from what is remaining until you get a 2. You continue ...
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### How do programs like BUGS/JAGS automatically determine conditional distributions for Gibbs sampling?

Seems like full conditionals are often quite difficult to derive, yet programs like JAGS and BUGS derive them automatically. Can someone explain how they algorithmically generate full conditionals for ...
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### Conditional probabilities - are they unique to Bayesianism?

I wonder whether conditional probabilities are unique to Bayesianism, or whether they are more of a general concept that is shared among several schools of thought among statistcs/probability people. ...
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