The statements you provided summarize important concepts in probability theory, particularly related to discrete uniform distributions. Here's a breakdown of each statement:
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All outcomes have the same probability: This is characteristic of a uniform distribution, where each possible outcome has an equal chance of occurring.
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The probability of each outcome is between 0 and 1: This is a fundamental property of probability measures; probabilities cannot be negative and cannot exceed 1.
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The sum of the probabilities is 1: This is a key axiom in probability theory, stating that the total probability of all possible outcomes in a sample space must equal 1.
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If the experiment is done repeatedly for n trials, then the expected number of times each outcome E would happen is given by n·(E): This is a reference to the expected value of a discrete random variable. In the case of independent trials of a uniform distribution, if each outcome has a probability \(E\), then in \(n\) trials, you would expect it to occur \(n \cdot E\) times.
Given this understanding, the statement "All of the above" is correct as it encompasses all the essential properties of a probability distribution.