PROBABILITIES Course

Distribution properties

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First, you should remember that a distribution must follow these criteria to be valid

  • the sum of all probabilities is 1
  • all values are in $[0,1]$

Independence

The independence between two distributions is defined the same as the independence between two variables. For instance for discrete variables, we have

  • $\mathbb{P}(X=x,\ Y=y) = \mathbb{P}(X=x) * \mathbb{P}(Y=y)$
  • $\mathbb{P}(X=x|Y=y) = \mathbb{P}(X=x)$
  • $\mathbb{P}(Y=y|X=x) = \mathbb{P}(Y=y)$