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Questions and Answers
In the experiment of tossing a coin 3 times, what is the sample space S?
In the experiment of tossing a coin 3 times, what is the sample space S?
- {HH, HT, TH, TT}
- {H, T}
- {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} (correct)
- {1, 2, 3}
What are the possible values of the discrete random variable X defined for the experiment of tossing a coin 3 times?
What are the possible values of the discrete random variable X defined for the experiment of tossing a coin 3 times?
- 0, 1, 2, 3 (correct)
- 1, 2, 3, 4
- 1, 2, 3
- 0, 1, 2
How is the function X defined for the experiment of tossing a coin 3 times?
How is the function X defined for the experiment of tossing a coin 3 times?
- X = the product of the outcomes
- X = the sum of the outcomes
- X = the number of heads appeared (correct)
- X = the average of the outcomes
What does it mean for a random variable to be discrete?
What does it mean for a random variable to be discrete?
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Why is the function X considered random?
Why is the function X considered random?
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Study Notes
Sample Space and Discrete Random Variable
- The sample space S for the experiment of tossing a coin 3 times is the set of all possible outcomes, which is {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}.
- The possible values of the discrete random variable X defined for the experiment of tossing a coin 3 times are the number of heads obtained in 3 tosses, which is {0, 1, 2, 3}.
- The function X is defined as X(w) = number of heads in outcome w, where w is an element of the sample space S.
- A random variable is discrete if it can only take on specific, distinct values.
- The function X is considered random because its outcome is uncertain until the experiment is performed, and it is based on the outcomes of the 3 coin tosses.
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