What is the expected value of a discrete uniform distribution on {1,2,3,4}?

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Multiple Choice

What is the expected value of a discrete uniform distribution on {1,2,3,4}?

Explanation:
For a discrete uniform distribution, every possible value occurs with the same probability, so the expected value is simply the average of all the possible outcomes. Compute the average of 1, 2, 3, and 4: (1 + 2 + 3 + 4) / 4 = 10 / 4 = 2.5. This result also aligns with the general fact that the mean of a uniform distribution from a to b is (a + b) / 2, here (1 + 4) / 2 = 2.5. The expectation is the long-run average you’d expect if you repeated the experiment many times, and it need not be one of the outcomes.

For a discrete uniform distribution, every possible value occurs with the same probability, so the expected value is simply the average of all the possible outcomes. Compute the average of 1, 2, 3, and 4: (1 + 2 + 3 + 4) / 4 = 10 / 4 = 2.5. This result also aligns with the general fact that the mean of a uniform distribution from a to b is (a + b) / 2, here (1 + 4) / 2 = 2.5. The expectation is the long-run average you’d expect if you repeated the experiment many times, and it need not be one of the outcomes.

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