The correct answer is: C. Both A and B
A discrete memoryless source is a source that produces a sequence of symbols, each of which is drawn from a finite set of symbols. The probability of each symbol depends only on the previous symbol, not on any other symbols in the sequence.
This means that the current letter produced by a discrete memoryless source is statistically independent of both the past output and the future output. In other words, the probability of the current letter does not depend on the previous letters, and it does not depend on the future letters.
Option A is correct because the current letter produced by a discrete memoryless source is statistically independent of the past output. This is because the probability of the current letter does not depend on the previous letters.
Option B is correct because the current letter produced by a discrete memoryless source is statistically independent of the future output. This is because the probability of the current letter does not depend on the future letters.
Option C is the correct answer because it includes both Option A and Option B.