大專statistics probability問題

(a) Two fair dice (of different colours) are rolled. Let X be the random variable
which denotes the maximum of the two numbers showing up on the dice (for
example, if the numbers ‘1’ and ‘2’ show up on the dice, then X = 2 ; if the same
number ‘1’ shows up on both dice, then X =1).

(i) Construct a probability distribution for X .

(ii) Calculate the mean, variance and standard deviation of the probability
distribution obtained in (a)(i).