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. | ||
+ | |||
+ | == 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: | ||
+ | |||
+ | {| class="wikitable" | ||
+ | |- | ||
+ | ! Event | ||
+ | ! Probability | ||
+ | ! Information (Surprise) | ||
+ | |- | ||
+ | |Someone tells you <math>1=1</math>. | ||
+ | |1 | ||
+ | |0 | ||
+ | |- | ||
+ | | You got the wrong answer on a 4-choice multiple choice question. | ||
+ | |<math>\tfrac{3}{4}</math> | ||
+ | |<math>\log_2\left(\frac{4}{3}\right)=0.415\,\mathrm{bits}</math> | ||
+ | |- | ||
+ | |} | ||
== 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)
-