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Chapter 9: Problem 465

Discuss and distinguish between discrete and continuous values.

Short Answer

Expert verified
Discrete and continuous values highlight two fundamentally different types of variables. Discrete values are distinct, separated values typically represented by integers or whole numbers. They represent countable events or items, for instance, the number of books on a shelf or people in a room. Conversely, continuous values can inhabit any value within a specific range and can be represented using real numbers or fractions. They often represent measurements or continuous data such as time, temperature, or distance. The key difference resides in the fact that discrete values are isolated and countable, while continuous values are unbroken and come in infinite number within a specific interval.

Step by step solution

01

Definition of Discrete values

Discrete values are isolated, distinct, and separate from each other, meaning they do not change continuously. Discrete values are typically integers or whole numbers, but they can also be other types of separated values.
02

Definition of Continuous values

Continuous values are variables that have an infinite number of possible values within a specific range. The values can change continuously from one point to another, with no interruptions, such as real numbers or decimals.
03

Example of Discrete values

A common example of discrete values is the number of people in a room. People can only be counted in whole, integer values (1, 2, 3, etc.) and there are no in-between values that make sense (e.g., there cannot be 1.5 people). Other examples include the number of books on a shelf, the number of students in a class, or the number of cars in a parking lot.
04

Example of Continuous values

A common example of continuous values is the amount of time it takes to complete a task, such as running a race or baking a cake. Time can be measured in fractions or decimals (e.g., 5.67 seconds, 12.4 minutes, etc.) and can take on any value within a specific range. Other examples include temperature, distance, and weight.
05

Key Differences between Discrete and Continuous Values

Discrete values are separate, whole numbers, while continuous values can take any value within a range and can be quantified in fractions or decimals. Discrete values tend to represent countable events or items, such as the number of people in a room or cars in a parking lot. Continuous values often represent measurements or continuous data over time, such as the amount of time it takes to complete a task, temperature, or distance.

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Most popular questions from this chapter

Consider the joint distribution of \(\mathrm{X}\) and \(\mathrm{Y}\) given in the form of a table below. The cell (i,j) corresponds to the joint probability that \(\mathrm{X}=\mathrm{i}, \mathrm{Y}=\mathrm{j}\), for \(\mathrm{i}=1,2,3, \mathrm{j}=1,2,3\) $$ \begin{array}{|c|c|c|c|} \hline \mathrm{Y}^{\mathrm{X}} & 1 & 2 & 3 \\ \hline 1 & 0 & 1 / 6 & 1 / 6 \\ \hline 2 & 1 / 6 & 0 & 1 / 6 \\ \hline 3 & 1 / 6 & 1 / 6 & 0 \\ \hline \end{array} $$ Check that this is a proper probability distribution. What is the marginal distribution of \(\mathrm{X} ?\) What is the marginal distribution of \(\mathrm{Y}\) ?

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