Heres the problem:

An experiment consists of rolling two fair six-sided dice and maximum value observed. Let random variable X represent this maximum value (for instance if on a toss one dice landed on 3 and the other dice landed on 4, the x = max(3,4) = 4.)

Note that X = {1,2,3,4,5,6}.

a) Construct a probability distribution for X. Hint: list all the possible outcomes and

which value of X each corresponds to.

b) Compute and interpret the expected value of X.

The table I made looks something like this:

Dice 1 - 1 2 3 4 5 6 2 3 4 5 6 3 4 5 6 4 5 6 5 6 6

Dice 2 - 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 4 4 4 5 5 6

X - 1 2 3 4 5 6 2 3 4 5 6 3 4 5 6 4 5 6 5 6 6

Any suggestions or hints would be highly appreciated! Thanks!