Question

The channel capacity maximized between input and output channels is equal to this quantity. For 10 points each:
[10h] Identify this quantity that measure how much observing one random variable informs you about another random variable. For two random variables X and Y, this quantity is equal to the sum of p(X,Y) ["p-of-x-y"] times log of P(X,Y) over P(X) ["p-of-x"] times P(Y) ["p-of-y"].
ANSWER: mutual information [prompt on information]
[10m] Mutual information is shown to be non-negative using this statement, which states that for a convex function phi, phi of the expectation value of X is less than or equal to the expectation value of phi of X.
ANSWER: Jensen’s inequality [or Jensen inequality]
[10e] Two answers required. The most commonly used unit for mutual information is a bit, the entropy for a variable that can be either of these two numbers. Binary representation of numbers uses these two digits to express any number.
ANSWER: 0 and 1
<Leo Law, Other Science>

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Summary

2023 Penn Bowl @ Waterloo10/28/2023Y120.00100%100%0%
2023 Penn Bowl (Harvard)10/21/2023Y110.00100%0%0%
2023 Penn Bowl (UK)10/28/2023Y520.00100%80%20%
2023 Penn Bowl @ UNC10/28/2023Y130.00100%100%100%

Data

Four Neg Omelette3HK1MM001010
EdinburghBroken Hearts0101020
Scottish, Irish, Both or Neither10 Negs that Shook the Quiz0101020
Betrayed by Rita IzzatdustTabearnacle10101030
Old London TownYes, Moderator0101020