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📗 [4 points] There are minions. They have either one eye or two eyes. They are either short or tall. Complete the two cells (enter ? then ??) in the following table so that the mutual information (i.e. information gain) between "Eyes" and "Height" is :
Number of minions
Eyes
Height
Examples
One
Short
Bob, Carl, Stuart
?
One
Tall
John
??
Two
Short
Dave, Jerry, Jorge
Two
Tall
Kevin, Tim, Tom
📗 Answer (comma separated vector): .
📗 [4 points] There are parrots. They have either a red beak or a black beak. They can either talk or not. Complete the two cells in the following table so that the mutual information (i.e. information gain) between "Beak" and "Talk" is :
Number of parrots
Beak
Talk
Red
Yes
?
Red
No
??
Black
Yes
Black
No
📗 Answer (comma separated vector): .
📗 [4 points] What is the conditional entropy \(H\left(B|A\right)\) for the following set of training examples.
item
A
B
1
2
3
4
5
6
7
8
📗 Answer: .
📗 [3 points] Statistically, cats are often hungry around 6:00 am (I am making this up). At that time, a cat is hungry of the time (C = 1), and not hungry of the time (C = 0). What is the entropy of the binary random variable C? Reminder that log based 2 of x can be found by log(x) / log(2) or log2(x).
📗 Answer: .
📗 [3 points] Statistically, December 18 is the cloudiest day of the year in Madison, Wisconsin. Your professor (not me, this is Professor Jerry Zhu's question) is not making this up. On that day, the sky is overcast, mostly cloudy, or partly cloudy of the time (C = 0), and clear or mostly clear of the time (C = 1). What is the entropy of the binary random variable C? Reminder that log based 2 of x can be found by log(x) / log(2).
📗 Answer: .
📗 [3 points] An UFO is hiding in a cloud near Haywood Ranch. On given day, the UFO hides in the cloud of the time (C = 0), and comes out of the cloud of the time (C = 1). What is the entropy of the binary random variable C? Reminder that log based 2 of x can be found by log(x) / log(2).
📗 Answer: .
📗 [3 points] A bag contains \(n\) = different colored balls. Randomly draw a ball from the bag with equal probability. What is the entropy of the outcome? Reminder that log based 2 of x can be found by log(x) / log(2) or log2(x).
📗 Answer: .
📗 [3 points] Statistically, December 18 is the cloudiest day of the year in Madison, Wisconsin. Your professor (not me, this is Professor Jerry Zhu's question) is not making this up. On that day, the sky is overcast, mostly cloudy, or partly cloudy of the time (C = 0), and clear or mostly clear of the time (C = 1). What is the entropy of the binary random variable C? Reminder that log based 2 of x can be found by log(x) / log(2).
📗 Answer: .
📗 [2 points] There is a total of red or green balls in a bag. How many red balls and how many green balls are there so that the entropy of the color of a randomly selected ball is imized?
📗 Answer (comma separated vector): .
📗 [3 points] The RDA Corporation has a prison with many cells. Without justification, you're about to be randomly thrown into a cell with equal probability. Cells to have Toruks that eat prisoners. Cells to are safe. With sufficient bribe, the warden will answer your question "Will I be in cell 1?" What's the mutual information (we call it information gain) between the warden's answer and your encounter with the Toruks? (I didn't write the stories in these questions, so I don't know the reference too.)
📗 Answer: .
📗 [4 points] It has a house with many doors. A random door is about to be opened with equal probability. Doors to have monsters that eat people. Doors to are safe. With sufficient bribe, Pennywise will answer your question "Will door 1 be opened?" What's the information gain (also called mutual information) between Pennywise's answer and your encounter with a monster?
📗 Answer: .
📗 [3 points] The RDA Corporation has a prison with many cells. Without justification, you're about to be randomly thrown into a cell with equal probability. Cells to have Toruks that eat prisoners. Cells to are safe. With sufficient bribe, the warden will answer your question "Will I be in cell 1?" What's the mutual information (we call it information gain) between the warden's answer and your encounter with the Toruks? (I didn't write the stories in these questions, so I don't know the reference too.)
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