The zebra plays a game in which in every turn she randomly chooses a letter from the set {A,B,C}, independently of other turns, and registers the outcome in a list. 1. Assume that the zebra plays exactly 4 turns, and let X denote the number of distinct outcomes she registers. 2. The first moment of X is 3. The probability that both A and B are registered at some point during the 4 turns she plays is 4. The second moment of X is

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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The zebra plays a game in which in every turn she randomly chooses a letter from the set {A,B,C},
independently of other turns, and registers the outcome in a list.
1. Assume that the zebra plays exactly 4 turns, and let X denote the number of distinct outcomes she
registers.
2. The first moment of X is
3. The probability that both A and B are registered at some point during the 4 turns she plays is
4. The second moment of X is
2. Now assume that the zebra plays until she registers every possible outcome at least once, that is, once she
has registered at least one of each of the outcomes she stops. The expected number of turns she plays is
Transcribed Image Text:The zebra plays a game in which in every turn she randomly chooses a letter from the set {A,B,C}, independently of other turns, and registers the outcome in a list. 1. Assume that the zebra plays exactly 4 turns, and let X denote the number of distinct outcomes she registers. 2. The first moment of X is 3. The probability that both A and B are registered at some point during the 4 turns she plays is 4. The second moment of X is 2. Now assume that the zebra plays until she registers every possible outcome at least once, that is, once she has registered at least one of each of the outcomes she stops. The expected number of turns she plays is
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