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.

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