 For a real observation space, the function formula_104 is a real-valued random variable if

This definition is a special case of the above because the set formula_106 generates the Borel σ-algebra on the set of real numbers, and it suffices to check measurability on any generating set.Here we can prove measurability on this generating set by using the fact that formula_107.The probability distribution of a random variable is often characterised by a small number of parameters, which also have a practical interpretation.