4.1 Probability Distribution Function (PDF) for a Discrete Random Variable
- Page ID
- 36483
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Learning Objective:
In this section, you will:
• Understand and apply the fundamentals of random variables and their probability distribution functions
A random variable describes the outcomes of a statistical experiment in words.
- Upper case letters such as X or Y denote a random variable.
- Lower case letters like x or y denote the value of a random variable.
A discrete probability distribution function (PDF) has two characteristics:
- Each probability is between zero and one, inclusive.
- The sum of the probabilities is one.
Example 1: A hospital researcher is interested in the number of times the average post-op patient will ring the nurse during a 12-hour shift. For a random sample of 50 patients, the following information was obtained.
|
X |
P(x) |
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0 |
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1 |
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2 |
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3 |
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4 |
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5 |
- Describe the random variable X in words.
- For this exercise, what are the values of x?
Notes 4.1
- What is the probability that the number of times a patient rings the nurse is 4?
- What is the probability that the number of times a patient rings the nurse is at least 4?
- What is the probability that the number of times a patient rings the nurse does not exceed 4?
- What is the probability that the number of times a patient rings the nurse is at least 1?
Example 2: Suppose Nancy has classes three days a week. She attends classes three days a week 80% of the time, two days 15% of the time, one day 4% of the time, and no days 1% of the time. Suppose one week is randomly selected.
- Describe the random variable X in words.
- For this exercise, what are the values of x?
- Suppose one week is randomly chosen. Construct a probability distribution table. What does the P(x) column sum to?
For more information and examples see online textbook OpenStax Introductory Statistics pages 244-246.
“Introduction to Statistics” by OpenStax, used is licensed under a Creative Commons Attribution