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This module introduces the Probability Distribution Function (PDF) and its characteristics.

A discrete probability distribution function has two characteristics:

  • Each probability is between 0 and 1, inclusive.
  • The sum of the probabilities is 1.

A child psychologist is interested in the number of times a newborn baby's crying wakes its mother after midnight. For a random sample of 50 mothers, the following information was obtained. Let X = the number of times a newborn wakes its mother after midnight. For this example, x = 0, 1, 2, 3, 4, 5.

P(x) = probability that X takes on a value x .

x P(x)
0 P(x=0) = 2 50
1 P(x=1) = 11 50
2 P(x=2) = 23 50
3 P(x=3) = 9 50
4 P(x=4) = 4 50
5 P(x=5) = 1 50

X takes on the values 0, 1, 2, 3, 4, 5. This is a discrete PDF because

  1. Each P(x) is between 0 and 1, inclusive.
  2. The sum of the probabilities is 1, that is,

2 50 + 11 50 + 23 50 + 9 50 + 4 50 + 1 50 = 1

Suppose Nancy has classes 3 days a week. She attends classes 3 days a week 80% of the time, 2 days 15% of the time, 1 day 4% of the time, and no days 1% of the time. Suppose one week is randomly selected.

Let X = the number of days Nancy ____________________ .

Let X = the number of days Nancy attends class per week .

X takes on what values?

0, 1, 2, and 3

Suppose one week is randomly chosen. Construct a probability distribution table (called a PDF table) like the one in the previous example. The table should have two columns labeled x and P(x) . What does the P(x) column sum to?

x P(x)
0 0.01
1 0.04
2 0.15
3 0.80
Practice Key Terms 1

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Source:  OpenStax, Elementary statistics. OpenStax CNX. Dec 30, 2013 Download for free at http://cnx.org/content/col10966/1.4
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