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Ch. 4 - Discrete Probability Distributions
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 4 - Discrete Probability DistributionsProblema 4.1.17
Capitolo 4, Problema 4.1.17

Discrete Variables and Continuous Variables In Exercises 13–18, determine whether the random variable x is discrete or continuous. Explain.
Let x represent the fitted hat sizes of members of a softball team.

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Understand the definitions of discrete and continuous variables: A discrete variable is one that can take on a countable number of distinct values (e.g., integers or specific categories), while a continuous variable can take on any value within a given range, often involving measurements (e.g., height, weight).
Identify the nature of the variable x in the problem: Here, x represents the fitted hat sizes of members of a softball team.
Consider how hat sizes are typically measured: Hat sizes are usually represented by specific numerical values or categories (e.g., 6, 6.5, 7, 7.5, etc.), which are countable and not infinitely divisible.
Determine whether the values of x are countable or continuous: Since hat sizes are chosen from a set of predefined, countable options, x is a discrete variable.
Conclude and explain: The random variable x is discrete because it represents a countable set of specific hat sizes rather than a continuous range of values.

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Discrete Variables

Discrete variables are those that can take on a countable number of distinct values. They often represent items that can be counted, such as the number of students in a class or the number of hats. In the context of the question, fitted hat sizes can be categorized into specific sizes (e.g., small, medium, large), making them discrete.
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Variance & Standard Deviation of Discrete Random Variables

Continuous Variables

Continuous variables, in contrast, can take on an infinite number of values within a given range. They are typically measurements that can be subdivided into finer increments, such as height or weight. If the variable were to represent something like the exact measurement of a hat size in inches, it would be considered continuous.
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Intro to Random Variables & Probability Distributions

Random Variables

A random variable is a variable whose values are determined by the outcomes of a random phenomenon. It can be classified as either discrete or continuous based on the nature of its possible values. In this case, the fitted hat sizes of team members represent a random variable that can be analyzed to determine its classification as discrete.
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Intro to Random Variables & Probability Distributions
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P(3) when μ = 6

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