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Probability Distributions - Oxford University Press

Probability Distributions - Oxford University Press

Probability Distributions - Oxford University

Probability Distributions 5 » Overview « The concept of probability is an important aspect of the study of statistics and within this chapter we shall introduce the reader to some of the concepts that are relevant to probability distributions. However, the main emphasis of the chapter is to focus on the concepts of discrete and continuous probability distributions and not on the fundamentals of probability theory. We will initially explore the issue of continuous probability distributions (normal) and then introduce the concept of discrete probability distributions (binomial, Poisson). Section 5.1 will provide a very brief introduction to the probability concepts and laws and Sections 5.2 and 5.3 will explore the concept of a probability distribution and introduce two distinct types: (a) continuous and (b) discrete. Table 5.1 summarizes the probability distributions that are applicable to whether the data variables are discrete/continuous and whether the distributions are symmetric/skewed. Variable type Measured characteristic Discrete Continuous Shape Symmetric Skewed Symmetric Skewed Distribution Binomial Poisson Normal Exponential Table 5.1 » Learning Objectives « On completing this chapter you should be able to: » Understand the concept of the following terms: experiment, outcome, sample space, relative frequency, and sample probability. » Understand the concept of events being mutually exclusive and independent. » Use the basic probability laws to solve simple problems. » Use tree diagrams (or decision trees) as an aid to the solution process. X Probability A probability provides a number value to the likely occurrence of a particular event. Continuous probability distribution If a random variable is a continuous variable, its probability distribution is called a continuous probability distribution. Discrete probability distribution If a random variable is a discrete variable, its probability distribution is called a discrete probability distribution. Sample space The sample space is an exhaustive list of all the possible outcomes of an experiment. Event An event is any collection of outcomes of an experiment.

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