Compute the mean and variances of the following discrete pro

Compute the mean and variances of the following discrete probability and distribution.
Compute the mean and variances of the following discrete probability distribution.

X                             P(x)
2                             .50
8                             .30
10                           .20

Please show work

Solution

mean = E[X] = 2*.5+8*.3+10*.2 = 5.4
variance = E[X2] - E[X]2
E[X2] = 4*.5+64*.3+100*.2 =41.2
Var(X) = 41.2 - 5.42 = 12.04