Difference between revisions of "161-A1.1"
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== Student Grading == | == Student Grading == | ||
− | How much information can we get from a single grade? Note that the maximum | + | How much information can we get from a single grade? Note that the maximum entropy occurs when all the grades have equal probability. |
* For Pass/Fail grades, the possible outcomes are: <math>\{\mathrm{P}, \mathrm{F}\}</math> with probabilities <math>\{\tfrac{1}{2}, \tfrac{1}{2}\}</math>. Thus, | * For Pass/Fail grades, the possible outcomes are: <math>\{\mathrm{P}, \mathrm{F}\}</math> with probabilities <math>\{\tfrac{1}{2}, \tfrac{1}{2}\}</math>. Thus, | ||
Revision as of 00:07, 14 September 2020
Let's look at a few applications of the concept of information and entropy.
Surprise! The Unexpected Observation
Information can be thought of as the amount of surprise at seeing an event. Note that a highly probable outcome is not surprising. Consider the following events:
Event | Probability | Information (Surprise) |
---|---|---|
Someone tells you . | ||
You got the wrong answer on a 4-choice multiple choice question. | ||
You got the correct answer in a True or False question. |
Student Grading
How much information can we get from a single grade? Note that the maximum entropy occurs when all the grades have equal probability.
- For Pass/Fail grades, the possible outcomes are: with probabilities . Thus,
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(1)
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- For grades = with probabilities , we get:
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(2)
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- For grades = with probabilities , we have:
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(3)
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- If we have all the possible grades with probabilities , we have:
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(4)
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