Odd entropy:-
Work example using the generalized entropy function G = 1 - max{p1, p2, p3, p4, p5, p6}. Find IG(X; Y) and I(X; Z). Which is greater and why? (The diligent professor) Professor Earnesto is designing a final exam for his class. He believes that 40 percent of the students are excellent and deserve As while the other, average, students deserve Bs.
However, Earnesto does not know which students are which. He is designing an exam that will help distinguish them, but currently he has two versions. For version 1, he believes that excellent students have a 70 percent chance of scoring high on the exam while only 30 percent of the average students will score high.
For version 2, he believes that 80 percent of the excellent students will score high, while 50 percent of the average students will score high. He intends to give As to those who score high and Bs to the others. Earnesto wants to maximize the match of grades: As to excellent students and Bs to average students. Which exam should he use, and in expected value terms, what percentage of grades will match?