Let the random variable x be equally likely to assume any of the values 1/12, 1/6, or 1/4. determine the mean and variance of x.

The mean of x is

(1/3) (1/12 + 1/6 + 1/4) = 1/6

The mean of the squares is

(1/3) ((1/12) ² + (1/6) ² + (1/4) ²) = 7/216

The variance is the difference between the mean square and the square of the mean.

7/216 - (1/6) ² = 1/216

The mean of x is 1/6.

The variance of x is 1/216.