In a Uniform Distribution over integers from a to b, what is true about the probabilities of outcomes?

In a Uniform Distribution over integers from a to b, what is true about the probabilities of outcomes?

• A. All outcomes have equal probability
• B. Probability increases with the value
• C. Probability decreases with the value
• D. Only boundary values have nonzero probability

Answer: (A)

In a discrete uniform distribution over integers from a to b, every value in the set {a, a+1, ..., b} is equally likely. There are b − a + 1 possible outcomes, and the total probability must sum to 1, so each outcome gets probability 1/(b − a + 1). That means all outcomes have equal probability, which is exactly what the uniform distribution prescribes. The other statements would imply a bias toward larger numbers or that only the endpoints can occur, but the defining feature here is that no value within the range is favored over another. Each value in the range occurs with the same chance.

In a discrete uniform distribution over integers from a to b, every value in the set {a, a+1, ..., b} is equally likely. There are b − a + 1 possible outcomes, and the total probability must sum to 1, so each outcome gets probability 1/(b − a + 1). That means all outcomes have equal probability, which is exactly what the uniform distribution prescribes.

The other statements would imply a bias toward larger numbers or that only the endpoints can occur, but the defining feature here is that no value within the range is favored over another. Each value in the range occurs with the same chance.