161-A1.1

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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)