Which of the following is correct about a probability distribution?
Click on the arrows to vote for the correct answer
A. B. C. D. E.Explanation
All describes properties of a probability distribution.
A probability distribution is a mathematical function or model that describes the likelihood of various outcomes in an uncertain or random event. It provides information about the probabilities associated with different possible outcomes.
Let's go through each answer option to determine which one is correct:
A. None of these answers: This option states that none of the other answer options are correct. We will evaluate the remaining answer options to see if any of them are correct.
B. Sum of the probabilities of all possible outcomes must equal 1: This statement is true for a valid probability distribution. In any probability distribution, the sum of the probabilities assigned to all possible outcomes must equal 1. This ensures that the total probability of all possible outcomes is accounted for and represents the entire sample space.
C. Probability of each outcome must be between 0 and 1 inclusive: This statement is also true for a valid probability distribution. The probability assigned to each outcome must be a non-negative value between 0 and 1, inclusive. Probabilities less than 0 or greater than 1 are not meaningful in the context of probability theory.
D. Outcomes must be mutually exclusive: This statement is not necessarily true for all probability distributions. In some cases, outcomes can be mutually exclusive, meaning that only one outcome can occur at a time. However, there are situations where outcomes can overlap or be non-mutually exclusive, such as in the case of dependent events or continuous probability distributions.
E. All of these answers: The correct answer is E. All of the statements mentioned in options B, C, and D are correct about a probability distribution. The sum of the probabilities of all possible outcomes must equal 1, the probability of each outcome must be between 0 and 1 inclusive, and while outcomes are often mutually exclusive, it is not a requirement for all probability distributions.
To summarize, the correct answer is E. All of these answers. A valid probability distribution requires the sum of probabilities to equal 1, the probability of each outcome to be between 0 and 1 inclusive, and there is no requirement for outcomes to be mutually exclusive in all cases.