Probability Distribution Function

The probability distribution function, P(x), of a discrete random variable X expresses the probability that X takes the value x, as a function of x.
That is,
                 P(x) = P(X = x),  for all values of x

Example: Rolling a Die (Probability Function Graph)
Graph the probability distribution function for the roll of a single six-sided balanced die.

Solution: Let the random variable X denote the number resulting from a single roll of a six-sided balanced die. Since

The function takes the value 0 for all other values of x, which cannot occur. The probability distribution function is graphed in the above figure,