Let the random variable x have a discrete uniform distribution on the integers 6 ≤ x ≤ 10. determine the mean, μ, and variance, σ2, of x.

Since the distribution is uniform, the mean is the average of the end values:
  μ = (6+10)/2 = 8

The mean square is
  (6² +7² +8² +9² +10²)/5 = 330/5 = 66
Then the variance is this value less the square of the mean
  σ² = 66-8² = 2

The solution to the system of equations (-2,2)