Statistics

Statistics

Chapter 5: Probability Distributions

The probability distribution is defined as the probability of a given or set of given outcomes will occur in a statistical experiment. As discussed in Chapter 4, probability is measured from 0 to 1; with 0 indicating that an outcome will not occur and 1 indicating that an outcome will occur. A probability of 1 would indicate that a given outcome would occur 100% of the time, this is a rare occurrence. This section will begin with a description of common types of probability distributions; pay particular attention to the application of each. As we progress, do not forget to refer back to Chapters 1 through 4. Keep in mind that we will only cover the major probability distributions, you may come across others.

Learning Objectives

After reading Chapter 5 and completing the workbook, you should be able to:

1. Explain the basic definitions of common terms used in probability. 2. Explain the different types of commonly encountered probability distributions. 3. Explain the application of the presented probability distributions.

Study Clues

A clear understanding of the basic statistical terms and concepts presented in Chapter 5 will help prepare you to advance in this course and learn more complex statistical calculations and specific statistical tests. You should refer back to Chapters 1 through 4 and understand all concepts presented thus far. As you study, you should pay particular attention definitions of the common types of probability distributions. You should be able to apply the probability distributions to specific statistical applications.

5.1 Basic Terms

• Discrete: Can represent an individual variable that is separate or acting separately from all other variables. • Finite: Is a mathematical number or function that has a countable end. If you had 10 coins, you have a finite number of coins (10). • Infinite: Is a mathematical measurement or function that does not have an end; meaning it can continue indefinitely.

5.2 Types of Distributions

• Bernoulli distribution: This classical probability distribution is easily calculated with the following formula: q = 1-p. A common example of this distribution is measuring the

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