Behaviour of a discret random variable

The likely behaviour of a discrete random variable X is determined by its probability function pX (also called the probability mass function or pmf), defined, for each possible value x which X can take, as

pX(x) = P(X = x).









Distribution function
The graph of the distribution function of a discrete random variable is flat, except for some upward jumps: the height of the jump at x is pX(x).


Probability function
Any sketch of the probability function should use bars or columns, since pX is equal to 0 everywhere except at the possible values of X.


http://www.staff.city.ac.uk/~sc397/courses/1ps/1ps03_5.htm