random variable (original) (raw)

A random variable X is said to be discrete if the set {X⁢(ω):ω∈Ω} (i.e. the range of X) is finite or countable. A more general version of this definition is as follows: A random variable X is discrete if there is a countable subset B of the range of X such that P(X∈B)=1 (Note that, as a countable subset of ℝ, B is measurable).

Example:

Consider the event of throwing a coin. Thus, Ω={H,T} where H is the event in which the coin falls head and T the event in which falls tails. Let X=number of tails in the experiment. Then X is a (discrete) random variable.