A random variable is a function that assigns a real number value to each outcome of an experiment involving chance. A random variable can be discrete, defined over a sample space with distinct outcomes, or continuous, defined over outcomes along a range. A probability distribution lists all possible outcomes of an experiment and their probabilities, with a discrete probability distribution specifically assigning probabilities to all values a discrete random variable can take.

1. A function whose value is a real number determined by each element in
the sample space is called a random variable. It is a quantity resulting
from an experiment that, by chance, can assume different values.
A random variable defined over a discrete sample space is called a
discrete random variable.
A random variable defined over a continuous sample space is called a
continuous random variable.
A probability distribution is a listing of all the outcomes of an experiment
and the probability associated with each outcome.
A table or formula listing all possible values that a discrete random
variable can take on, along with the associated probabilities, is called a
discrete probability distribution.