Number of Random Variables
- univariate probability distribution - sample space is a univariate random variable (one-dimensional variable)
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joint probability distribution (compound probability distribution) - refers to the probability distribution of 2 or more random variables occurring together
- multivariate joint probability distribution - sample space is a multivariate random variable (2 or more dimensions/variables) (e.g. the probability of 𝐴 and 𝐵 and 𝐶, denoted 𝐏(𝐴,𝐵,𝐶))
- bivariate joint probability distribution - sample space is a bivariate random variable (two-dimensional variables) (e.g. the probability of 𝐴 and 𝐵, denoted 𝐏(𝐴,𝐵))
- full joint probability distribution - refers to a probability distribution of all random variables in a given domain
- multivariate joint probability distribution - sample space is a multivariate random variable (2 or more dimensions/variables) (e.g. the probability of 𝐴 and 𝐵 and 𝐶, denoted 𝐏(𝐴,𝐵,𝐶))
the following imply each other:
- 𝐏(𝐴,𝐵) = 𝐏(𝐵,𝐴) = 𝐏(𝐵|𝐴)𝐏(𝐴) = 𝐏(𝐴|𝐵)𝐏(𝐵) # product rule
- 𝐏(𝐵|𝐴)𝐏(𝐴) = 𝐏(𝐴|𝐵)𝐏(𝐵)/𝐏(𝐴) # Baye’s Theorem