Discrete Probability Distributions

Probability function, probability mass function, or probability distribution is used to calculate probabilities associated with discrete random variables.  It is directly driven from the definition of the random variable. 

For convenience, we shall denote a random variable by a capital letter, while the corresponding small letter will be used to denote a specific value of the random variable.  For example, X may represent the number of students passing a course. x then, will denote a specific value of X.  The probability function will be denoted by p(x), where p(x) will assign P [X = x].

L. K. Gaafar