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The lecturer models English text as a Markov chain where the probability of the next character X depends on the previous character Y. By conditioning on context, such as knowing the previous letter is Q, the uncertainty about the next letter (often U) is greatly reduced, demonstrating how conditional entropy H(X|Y) lowers average code length.

Conditions: The source is English text.; The previous character is treated as conditioning information for the next character.

The lecturer models English text as a Markov chain where the probability of the next character X depends on the previous character Y. By conditioning on context, such as knowing the previous letter is Q, the uncertainty about the next letter (often U) is greatly reduced, demonstrating how conditional entropy H(X|Y) lowers average code length.

Conditions: The source is English text.; The previous character is treated as conditioning information for the next character.

When conditional entropy H(X|Y) is zero, it means there is no remaining uncertainty or surprise about X once Y is known. This implies that X is a deterministic function of Y, so all information about X is completely contained within Y.

Conditions: X and Y are discrete random variables.

When conditional entropy H(X|Y) is zero, it means there is no remaining uncertainty or surprise about X once Y is known. This implies that X is a deterministic function of Y, so all information about X is completely contained within Y.

Conditions: X and Y are discrete random variables.