When two dice are thrown let X be the larger of the two numbers on the two throws find the probability distribution mean and variance of X?

The probability distribution is

P(X = 1) = 1/36

P(X = 2) = 3/36

P(X = 3) = 5/36

P(X = 4) = 7/36

P(X = 5) = 9/36

P(X = 6) = 11/36

P = 0 otherwise.

Mean(X) = 4.4722

Variance = 1.9715