CK-12 Probability and Statistics - Advanced

4.2. Probability Distribution for a Discrete Random Variable http://www.ck12.org

P(x= 0 ) =P(T T) = 1 / 4

P(x= 1 ) =P(HT)+P(T H) = 1 / 4 + 1 / 4 = 1 / 2

P(x= 2 ) =P(HH) = 1 / 4

Thus, we have just had a complete description of the values of the random variables and have calculated the
associated probabilities that are distributed over these values. We refer to it as theprobability distribution.
This probability distribution can be represented in different ways, sometimes in a tabular form and sometimes in
a graphical one. Both forms are shown below.

In tabular form,

x P(x)

0 1 / 4

1 1 / 2

2 1 / 4

Figure:The Tabular Form of the Probability Distribution for the Random Variable in the First Example.

In a graphical form,

We can also describe the probability distribution in a mathematical formula, which we will do later in the chapter.

Probability Distribution

The probability distribution of a discrete random variable is a graph, a table, or a formula that specifies the probability
associated with each possible value that the random variable can assume.

Two conditions must be satisfied for all probability distributions:

Two conditions must be satisfied for the probability distribution: