Let X equal the larger outcome when a pair of fair foursided

Let X equal the larger outcome when a pair of fair four-sided dice is rolled. The pmf of X is

x=1,2,3,4

Find the mean, variance and standard deviation of X.

Solution

Plugging in the values of x to f(x) to get the probabilities, consider the table:

Thus,          
          
E(x) = Expected value = mean =    3.125   [ANSWER, MEAN]  

Var(x) = E(x^2) - E(x)^2 =    0.859375   [ANSWER, VARIANCE]  

s(x) = sqrt [Var(x)] =    0.927024811   [ANSWER, STANDARD DEVIATION]