Difference between revisions of "161-A1.1"
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Line 17: | Line 17: | ||
|<math>\frac{3}{4}</math> | |<math>\frac{3}{4}</math> | ||
|<math>\log_2\left(\frac{4}{3}\right)=0.415\,\mathrm{bits}</math> | |<math>\log_2\left(\frac{4}{3}\right)=0.415\,\mathrm{bits}</math> | ||
+ | |- | ||
+ | | You guessed correctly on a 4-choice multiple choice question. | ||
+ | |<math>\frac{1}{4}</math> | ||
+ | |<math>\log_2\left(4\right)=2\,\mathrm{bits}</math> | ||
|- | |- | ||
| You got the correct answer in a True or False question. | | You got the correct answer in a True or False question. |
Revision as of 00:08, 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 guessed correctly 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,
-
(1)
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- For grades = with probabilities , we get:
-
(2)
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- For grades = with probabilities , we have:
-
(3)
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- If we have all the possible grades with probabilities , we have:
-
(4)
-