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Joint probability distribution of several random variables gives the probability that all of them simultaneously lie in a particular region.
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Multimodality from unimodal variables
Let's say a data matrix $\bf{X} \in \mathbb{R}^{N \times D}$ has $D$ random variables each with $N$ observations. So $j$th column of $\bf{X}$ is $N$ observations of $j$th random variable.
Suppose th …