Question

Let the random variable x have a discrete uniform distribution on the integers 8 ≤ x ≤ 10. determine the mean, μ, and variance, σ2, of x.

Answer 1

The discrete uniform distribution is on the interval 8 ≤ x ≤ 10.
Therefore the probability density function (shown in the figure) is
P(x) = 1/3 = 1/3 for x = 8, 9, 10
       = 0 otherwse

The mean is μ = 1/3.

The variance is 
σ² = Σp(x) (x- μ)²

Because x - μ = 0 for x = 8,9,10, therefore
σ² = 0

Answer:
μ = 1/3
σ² = 0