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96 CHAPTER 4 PROBABILITY DISTRIBUTIONS
0.25
0.20
Probability
0.15
0.10
0.05
0.00
1 2 3 4 5 6 7 8
x (number of assistance programs)
FIGURE 4.2.1 Graphical representation of the probability
distribution shown in Table 4.2.1.
variable X, then we may then give the following two essential properties of a probability
distribution of a discrete variable:
(1)
(2)
0 … P1X = x2 … 1
a P1X = x2 = 1, for all x
The reader will also note that each of the probabilities in Table 4.2.2 is the
relative frequency of occurrence of the corresponding value of X.
With its probability distribution available to us, we can make probability statements
regarding the random variable X. We illustrate with some examples.
EXAMPLE 4.2.2
What is the probability that a randomly selected family used three assistance
programs
Solution: We may write the desired probability as p132 = P1X = 32. We see in
Table 4.2.2 that the answer is .1313.
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EXAMPLE 4.2.3
What is the probability that a randomly selected family used either one or two programs
Solution:
To answer this question, we use the addition rule for mutually exclusive
events. Using probability notation and the results in Table 4.2.2, we write the
answer as P11 ´ 22 = P112 + P122 = .2088 + .1582 = .3670. ■