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Tagged with conditional-independence distributions
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Join distribution of independent random variables that aren't conditionally independent
I am asked to give an example for a joint distribution of three random variables, $U$, $V$ and $W$, where $U$ and $V$ are (unconditionally) independent but are NOT conditionally independent given $W$.
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Is it always possible to find a joint distribution $p(x_1,x_2,x_3,x_4)$ consistent with these local conditional distributions?
I am currently studying Bayesian Reasoning and Machine Learning by David Barber, the 4th chapter exercise 4.1 (p 79). The exercise is the following:
Exercise 4.1
Consider the pairwise Markov network,
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Sampling with fixed probability from two different distributions. How is the sample distributed?
Let
$(\Omega,\mathcal A,\operatorname P)$ be a probability space
$\mu$ be a probability measure on $(\mathbb R,\mathcal B(\mathbb R))$
$X$ be real-valued random variable on $(\Omega,\mathcal A,\...
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conditional probability involving mixed variable types
I'm trying to answer the following question
A defective coin minting machine produces coins whose probability of heads is a random variable $T$ with PDF $f_{T}(p) = 1+\mathrm{sin}(2\pi p)$ if $p \in ...
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