Random Variables
Easymathematics
The sum of all probabilities in a probability distribution equals
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Solution
Incorrect! Answer:
1
- Total Certainty: A probability distribution assigns probabilities to all possible outcomes of an experiment. Since one of these outcomes must occur, the total probability is certainty.
- Axiom: ∑P(X=xi)=1.
- Continuous Case: ∫−∞∞f(x)dx=1.
- Conclusion: The total area under a probability density curve or sum of discrete mass is always 1.
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About This Question
- Subject
- mathematics
- Chapter
- statistics and probability
- Topic
- random variables
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
1
- Total Certainty: A probability distribution assigns probabilities to all possible outcomes of an experiment. Since one of these outcomes must occur, the total probability is certainty.
- Axiom: ∑P(X=xi)=1.
- Continuous Case: ∫−∞∞f(x)dx=1.
- Conclusion: The total area under a probability density curve or sum of discrete mass is always 1.
This easy difficulty mathematics question is from the chapter statistics and probability, covering the topic of random variables. It appeared in the 2025 exam.
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