Difference between revisions of "161-A1.1"

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Let's look at a few applications of the concept of information and entropy.
 
Let's look at a few applications of the concept of information and entropy.
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== Surprise! The Unexpected Observation ==
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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:
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{| class="wikitable"
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|-
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! Event
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! Probability
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! Information (Surprise)
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|-
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|Someone tells you <math>1=1</math>.
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|1
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|0
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|-
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| You got the wrong answer on a 4-choice multiple choice question.
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|<math>\tfrac{3}{4}</math>
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|<math>\log_2\left(\frac{4}{3}\right)=0.415\,\mathrm{bits}</math>
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|-
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|}
  
 
== Student Grading ==
 
== Student Grading ==

Revision as of 00:03, 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 . 1 0
You got the wrong answer on a 4-choice multiple choice question.

Student Grading

How much information can we get from a single grade? Note that the maximum information occurs when all the grades have equal probability.

  • For Pass/Fail grades, the possible outcomes are: with probabilities . Thus,

 

 

 

 

(1)

  • For grades = with probabilities , we get:

 

 

 

 

(2)

  • For grades = with probabilities , we have:

 

 

 

 

(3)

  • If we have all the possible grades with probabilities , we have:

 

 

 

 

(4)