Question

Now, the bin contains 12 green balls. In each event, you pick one ball from the bin and observe the color of the ball. The balls are only distinguishable with their colors. After observation, you put the ball back into the bin. What is the entropy value for five events in bits?

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mathstatistics and probabilitystatistics and probability questions and answersInformation Entropy Problem 2. Balls In A Bin Suppose There Are Five Red Balls, Three Yellow ...

Question: Information Entropy Problem 2. Balls In A Bin Suppose There Are Five Red Balls, Three Yellow Balls, And Four Green Balls In A Bin. In Each Event, You Pick One Ball From The Bin And Observe The Color Of The Ball (the Balls Are Only Distinguishable By Their Colors). After Observation, You Put The Ball Back Into The Bin. A. What Is The Information Entropy ...

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Information Entropy

Problem 2. Balls in a Bin

Suppose there are five red balls, three yellow balls, and four green balls in a bin. In each event, you pick one ball from the bin and observe the color of the ball (the balls are only distinguishable by their colors). After observation, you put the ball back into the bin.

a. What is the information entropy value for an event?

b. What is the information entropy for five events?

c. Now you add two additional yellow balls in the bin and conduct the events. What is the value of the entropy for an event?

d. From Problem c. (with a total of fourteen balls in the bin), you can either add one ball of any color to the bin or subtract one ball of any color from the bin. What would your action be (add or subtract and which color) to maximize the entropy of the events?