Random Variables
The sum of all probabilities in a probability distribution equals
Select the correct option:
🔒 Solution Hidden from View
Submit your answer to unlock the detailed step-by-step solution.
More statistics and probability Practice Questions
From a committee containing seven men and five women, a subcommittee of three persons is selected at...
From a committee containing seven men and five women, a subcommittee of three persons is selected at...
When every observation in a dataset is first multiplied by three and then increased by five, how doe...
When every observation in a dataset is first multiplied by three and then increased by five, how doe...
An urn holds four red and six blue balls, and one ball drawn at the first stage is set aside without...
An urn holds four red and six blue balls, and one ball drawn at the first stage is set aside without...
A binomial random variable representing successes in n trials has mean equal to 4 and variance equal...
A binomial random variable representing successes in n trials has mean equal to 4 and variance equal...
Suppose events A and B satisfy P(A) = 1/2, P(B) = 1/3, and the conditional probability P(A given B) ...
Suppose events A and B satisfy P(A) = 1/2, P(B) = 1/3, and the conditional probability P(A given B) ...
A group of ten numbers has a recorded mean of fifteen, but later one entry originally read as eight ...
A group of ten numbers has a recorded mean of fifteen, but later one entry originally read as eight ...
Two friends agree to meet between five and six o'clock, each arriving at a uniformly random time and...
Two friends agree to meet between five and six o'clock, each arriving at a uniformly random time and...
A diagnostic test detects a disease present in one percent of a population with sensitivity ninety-n...
A diagnostic test detects a disease present in one percent of a population with sensitivity ninety-n...
A fair six-faced die is rolled once and the random variable X equals the number shown on the top fac...
A fair six-faced die is rolled once and the random variable X equals the number shown on the top fac...
In a binomial setting where a marksman hits a target with probability 1/4 on each independent shot, ...
In a binomial setting where a marksman hits a target with probability 1/4 on each independent shot, ...
Two distinct groups contain twenty and thirty students with mean marks of sixty and seventy respecti...
Two distinct groups contain twenty and thirty students with mean marks of sixty and seventy respecti...
Two players alternately roll a fair die starting with the first player, and whoever first rolls a si...
Two players alternately roll a fair die starting with the first player, and whoever first rolls a si...
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.
Looking for more practice? Explore all mathematics questions or browse statistics and probability questions on RankGuru.