Question at position 33 True/False Question: The entropy of a homogeneous set (a set of instances with the same label) is not always zero. TrueFalse

Question

BlackTom AI · Accepted Answer

Consider the claim about entropy for a homogeneous set, and examine each option carefully.
Option 1: 'True' — This statement would mean that a dataset where all instances share the same label can have nonzero entropy. In information theory, a completely uniform (homogeneous) distribution over classes yields maximum predictability for the single observed label, and thus zero entropy. Therefore, asserting that the entropy is not always zero is incorrect because, by definition, H = - sum p(i) log p(i) equals 0 when one class has probability 1 and all others have probability 0.
Option 2: 'False' — This aligns with the standard entropy calculation. Since a homogeneous set has p = 1 for the single label, the entropy H = -1 * log(1) = 0. There is no randomness across labels to contribute to uncertainty, so the entropy is zero. Any claim that entropy could be nonzero in this case contradicts the fundamental formula for entropy of a categorical distribution.

Question at position 33 True/False Question: The entropy of a homogeneous set (a set of instances with the same label) is not always zero. TrueFalse

View Explanation

Log in for full answers

Similar Questions

Consider the following dataset with features X, Y and Z [table] X | Y | Z Jack | 0 | A Jack | 1 | B Amy | 0 | A Amy | 1 | B Sam | 0 | B Sam | 1 | B [/table] Let H denote the entropy function. Which of the following is true?

Consider the following dataset with features X, Y and Z [table] X | Y | Z Jack | 0 | A Jack | 1 | B Amy | 0 | A Amy | 1 | B Sam | 0 | B Sam | 1 | B [/table] Let [math: H] denote the entropy function. Which of the following is true?

Consider the following dataset with features X, Y and Z [table] X | Y | Z Jack | 0 | A Jack | 1 | B Amy | 0 | A Amy | 1 | B Sam | 0 | B Sam | 1 | B [/table] Let H denote the entropy function. Which of the following is true?

Consider the following dataset with features X, Y and Z [table] X | Y | Z 0 | 0 | 0 0 | 1 | 1 1 | 0 | 0 1 | 1 | 1 2 | 0 | 1 2 | 1 | 1 [/table] Compute the entropy of [math: XYZ+1]\frac{XY}{Z+1}

Consider the following dataset with features X, Y and Z [table] X | Y | Z Jack | 0 | A Jack | 1 | B Amy | 0 | A Amy | 1 | B Sam | 0 | B Sam | 1 | B [/table] Let [math: H] denote the entropy function. Which of the following is true?

Consider the following dataset with features X, Y and Z [table] X | Y | Z 0 | 0 | 0 0 | 1 | 1 1 | 0 | 0 1 | 1 | 1 2 | 0 | 1 2 | 1 | 1 [/table] Compute the entropy of [math: XYZ+1]\frac{XY}{Z+1}

Question at position 16 Multiple Choice Question: Entropy can be negativeis used to calculate information gainis a measure of information gainis a measure of correlation between numeric variables

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler