When using a discrete uniform distribution for the number of bidders, which statement is true?

When using a discrete uniform distribution for the number of bidders, which statement is true?

• A. Each possible bid amount has equal probability
• B. Distributions is continuous
• C. Each integer value in the defined range has equal probability
• D. The expected number of bidders is fixed

Answer: (C)

In a discrete uniform distribution, every value the variable can take within its defined range is equally likely. For the number of bidders, the variable can be any integer within the specified range, so each integer value in that range has the same probability, namely 1 divided by the number of integers in the range. That’s why the true statement is that each integer value in the defined range has equal probability. This differs from a continuous case, where outcomes form an interval of real numbers and probabilities are spread continuously. The idea that each possible bid amount has equal probability would apply to the bid amount itself, not to the count of bidders. And while the expected number of bidders is a fixed constant determined by the range (the average of the endpoints), the essential defining feature of the discrete uniform is the equal likelihood of each integer in the range.

In a discrete uniform distribution, every value the variable can take within its defined range is equally likely. For the number of bidders, the variable can be any integer within the specified range, so each integer value in that range has the same probability, namely 1 divided by the number of integers in the range. That’s why the true statement is that each integer value in the defined range has equal probability.

This differs from a continuous case, where outcomes form an interval of real numbers and probabilities are spread continuously. The idea that each possible bid amount has equal probability would apply to the bid amount itself, not to the count of bidders. And while the expected number of bidders is a fixed constant determined by the range (the average of the endpoints), the essential defining feature of the discrete uniform is the equal likelihood of each integer in the range.