A random variable is a function that can take
on values corresponding to a sample point in a sample space. As
each sample point is associated with a probability value, random
variables assumes its values with a certain probability that
depends on the sample point on which the value is based. A random
variable that is defined over a discrete sample space has a
finite or countable number of possible values and is called a discrete
random variable. A random variable that is defined over
a continuous sample space has an infinite set of possible values
and is called a continuous random variable.
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