What is the expected value of a uniform distribution defined as?

What is the expected value of a uniform distribution defined as?

• A. E(x) = (b-a)/2
• B. E(x) = (b+a)/2
• C. E(x) = a + b
• D. E(x) = (b²-a²)/2

Answer: (B)

The expected value for a uniform distribution defined on the interval [a, b] is given by the formula E(x) = (b + a) / 2. This formula reflects the central point of the interval, which is intuitive when considering that a uniform distribution assumes all outcomes between a and b are equally likely. The interval encompasses all values from a to b, and the average of those two endpoints gives us the mean or expected value. By combining b and a and dividing by 2, we effectively compute the midpoint of the segment, which represents the expected outcome of a random variable uniformly distributed over that range. In this context, the other options do not accurately represent the calculation for the expected value of a uniform distribution, as they either represent different concepts or do not conform to the definition of the uniform distribution.

The expected value for a uniform distribution defined on the interval [a, b] is given by the formula E(x) = (b + a) / 2. This formula reflects the central point of the interval, which is intuitive when considering that a uniform distribution assumes all outcomes between a and b are equally likely.

The interval encompasses all values from a to b, and the average of those two endpoints gives us the mean or expected value. By combining b and a and dividing by 2, we effectively compute the midpoint of the segment, which represents the expected outcome of a random variable uniformly distributed over that range.

In this context, the other options do not accurately represent the calculation for the expected value of a uniform distribution, as they either represent different concepts or do not conform to the definition of the uniform distribution.