Article 1663932435724Subject 2. Probability Function
Every random variable is associated with a probability distribution that describes the variable completely. A probability function is one way to view a probability distribution. It specifies the probability that the random variable takes on a specific value; P(X = x) is the probability that a random variable X takes on the value x.
A probability function has two key properties:
0 ≤ P(X=x) ≤ 1, because probability is a number between 0 and 1.
ΣP(X=x) = 1. The sum of the probabilities P(X=x) over all values of X equals 1. If there is an exhaustive list of the distinct possible outcomes of a random variable and the probabilities of each are added up, the probabilities must sum to 1.
The following examples will utilize these two properties in order to examine whether they are probability functions.
p(x) = x/6 for X = 1, 2, 3, and p(x) = 0 otherwise
Substituting into p(x): p(1) = 1/6, p(2) = 2/6 and p(3) = 3/6
Note that it is not necessary to substitute in a