Random Variables
Lesson 5 Chapter 2
In probability theory, the outcomes of a random phenomenon determine the random variable values. In other words, a random variable is a variable that its values are determined with a random event. We should be able to measure a random variable that provides the capability to assign probabilities to its possible values. The domain of a random variable is the sample space. For example, in the case of having a dice, only six possible outcomes are considered, as {1,2,3,4,5,6}.
By using more precise mathematics notation, a random variable is a measurable function defined as
, which is from all possible space
to some event
. Let's have an illustrative example. Assume we would like to roll a dice, and the measurable event space is all numbers less than 4. Here, we have
, the random variable
as the outcome of rolling the dice, and we define the event as
.
