5-1 Probability Distributions 205 Key Concept This section introduces the concept of a random variable and the concept of a probability distribution. We illustrate how a probability histogram is a graph that visually depicts a probability distribution. We show how to find the important parameters of mean, standard deviation, and variance for a probability distribution. Most importantly, we describe how to determine whether outcomes are significantly low or significantly high or neither. We begin with the related concepts of random variable and probability distribution. 5-1 Probability Distributions of this book and the core of inferential statistics are based on applications of probability distributions. In this chapter we focus on discrete probability distributions. Here are the chapter objectives: 5-1 Probability Distributions • Define random variable and probability distribution. • Determine whether the requirements of a probability distribution are satisfied when given values of a random variable along with their corresponding probabilities. • Compute the mean and standard deviation of a probability distribution. The mean and standard deviation can then be used to determine whether results are significantly low or significantly high. 5-2 Binomial Probability Distributions • Describe a binomial probability distribution and find probability values for a binomial distribution. • Compute the mean and standard deviation for a binomial distribution, and then use those results to determine whether results are significantly low or significantly high. 5-3 Poisson Probability Distributions • Describe a Poisson probability distribution and find probability values for a Poisson distribution. w significantly high w significantly high In Section 1-2 we made a distinction between discrete and continuous data. Random variables may also be discrete or continuous, and the following two definitions are consistent with those given in Section 1-2. PART 1 Basic Concepts of a Probability Distribution DEFINITIONS A random variable is a variable (typically represented by x) that has a single numerical value, determined by chance, for each outcome of a procedure. A probability distribution is a description that gives the probability for each value of the random variable. It is often expressed in the format of a table, formula, or graph.
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