Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

5. Binomial Distribution & Discrete Random Variables

Discrete Random Variables

Statistics

5. Binomial Distribution & Discrete Random Variables

Discrete Random Variables

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2:06 minutes

Problem 4.R.1

Textbook Question

In Exercises 1 and 2, determine whether the random variable x is discrete or continuous. Explain.

Let x represent the grade on an exam worth a total of 100 points.

Verified step by step guidance

Understand the definitions: A discrete random variable takes on a countable number of distinct values, while a continuous random variable can take on any value within a given range, including fractions and decimals.

Identify the nature of the variable x: The grade on an exam worth a total of 100 points is typically expressed as a whole number (e.g., 85, 90, etc.), which suggests it is countable.

Consider whether fractional values are possible: If grades are rounded to whole numbers, x is discrete. However, if fractional grades (e.g., 85.5) are allowed, x could be continuous.

Determine the context: In most grading systems, grades are reported as whole numbers, making x a discrete random variable.

Explain the conclusion: Since the grade is typically a countable value and does not take on an infinite range of possibilities within an interval, x is classified as a discrete random variable.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Discrete Random Variable

A discrete random variable is one that can take on a countable number of distinct values. Examples include the number of students in a class or the outcome of rolling a die. In the context of grades, if we consider only whole number scores (0, 1, 2, ..., 100), the variable is discrete because it cannot take on values like 75.5.

Continuous Random Variable

A continuous random variable can take on an infinite number of values within a given range. This means it can represent measurements that can be infinitely divided, such as height or weight. If grades were measured with decimals (e.g., 75.5), then the variable would be considered continuous, as it could take any value within the range of possible scores.

Random Variable

A random variable is a numerical outcome of a random phenomenon. It can be classified as either discrete or continuous based on the nature of its possible values. Understanding whether a random variable is discrete or continuous is crucial for selecting appropriate statistical methods for analysis, such as probability distributions.

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