If is a probability space, then a random variable on is a measurable function to a measurable space (frequently taken to be the real numbers with the standard measure). The law of a random variable is the probability measure defined by .
A random variable is said to be discrete if the set (i.e. the range of ) is finite or countable. A more general version of this definition is as follows: A random variable is discrete if there is a countable subset of the range of such that (Note that, as a countable subset of , is measurable).
Consider the event of throwing a coin. Thus, where is the event in which the coin falls head and the event in which falls tails. Let number of tails in the experiment. Then is a (discrete) random variable.
|Date of creation||2013-03-22 11:53:10|
|Last modified on||2013-03-22 11:53:10|
|Last modified by||mathcam (2727)|
|Defines||discrete random variable|
|Defines||continuous random variable|
|Defines||law of a random variable|