# 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 three prisoners (Statistical Inference - Cassella and Berger)

There are quite a few questions regarding three prisoners riddle, but my question relating to a particular line of reasoning from Cassella and Berger, as highlighted in the image below. Could you ...
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### How to calculate Bayes factor for conditional probability?

I have a data set of 1000 drug-effect pairs. I am trying to identify which drug is most likely given the observed effect. My original approach was to calculate $P\left(d_j | e_i\right)$ for each ...
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### Probability of a girl given 2 boys [closed]

I recently had a test on Probability Distributions and got this question wrong. Some help would be appreciated. If I recall correctly, the question was : In a family of 4 children, the probability ...
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### How do I factor this conditional probability?

I am having a brain freeze. Could you show the steps to get from line 1 to line 2? Thanks!
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### Given distribution of $X$ and $X|Y=y$, is it possible to find distribution of $Y$?

What the title says! My intuition is NO since in Bayesian statistics we typically specify the prior and likelihood, and from those two we can compute the posterior and so on. We can interpret $Y$ = ...
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### Estimate random effects for a new individual with a linear mixed effects model

Consider repeated observations $\mathcal{Y} = (y_{i,j})_{i,j}$ obtained for $p$ individuals ($1 \leq i \leq p$), at different time points $t_{i,j}$ $(1 \leq j \leq n_i$). The "random slope and ...
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### Estimating mean of a normal distribution from a distribution of means

There are $i$ number of normal distributions $Y_i\sim N(\mu_i, 8^2)$. The means of all the $i$ distributions form another normal distribution $X\sim N(85, 2.5^2)$. Suppose a distribution $Y_i$ is ...
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### Intutitive meaning behind the formal definition of sufficient statistic?

According to the definition of sufficiency, a statistic is sufficient for a parameter if the conditional distribution of $X$ given a value of statistic does not depend upon the parameter. What I am ...
For my textbook, Introduction to Probability by Blitzstein and Hwang, I have the problem where I have the random variables $X$, $Y$, and $Z$ such that $X \sim N(0, 1)$. I am also told that, ...