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A 'random variable' means a numerical description of the outcome of a statistical experiment. A random variable that may assume only a finite number or an infinite sequence of values is said to be discrete; one that may assume any value in some interval on the real number line is said to be continuous.

A discrete distribution describes the probability of occurrence of each value of a discrete random variable.

On the other hand, a binomial random variable is the number of successes 'x' in 'n' repeated trials of a binomial experiment. The probability distribution of a binomial random variable is called a binomial distribution.