Final answer:
The mean of a discrete uniform distribution is calculated as (a + b) / 2, and the variance is found using the formula ((b - a + 1)² - 1) / 12.
Step-by-step explanation:
Calculating Mean and Variance of a Discrete Uniform Distribution
The mean (expected value) of a discrete uniform distribution for a random variable X can be calculated using the formula μ = (a + b) / 2, which is derived from the sum of the smallest number in the range (a) and the largest number (b), divided by 2. To find the variance, we use σ² = (b - a + 1)² - 1) / 12. The variance formula comes from the range (b - a + 1), which indicates the number of possible values that X can take on, squared and then subtracting 1, finally divided by 12.
To provide an example, if a = 3 and b = 6 for the discrete random variable X, the mean would be calculated as μ = (3 + 6) / 2 = 4.5. The variance would be σ² = ((6 - 3 + 1)² - 1) / 12 = (16 - 1) / 12 = 15 / 12 = 1.25.