Statistics Expected Variable Question

[thomas49th]

Homework Statement

Y is the larger score showing when two dice are thrown
Calculate E(Y)

Homework Equations

Presume the dice are fair

The Attempt at a Solution

Hmm not sure. I've listed combinations of throw events on paper but I don't think that will help. Y can never be 1. Y can never be the same as the other die?
Do I want to draw a probability distrubution table?

I've been messing around with it for a while with not much progress

Thanks :)

 

[Mark44]

If both dice come up with 1s, if you don't count the 1, you won't have anything to count for that roll.

With two dice, there are 36 possible outcomes: {(1, 1), (1, 2), ... , (1, 6), (2, 1), ... (2, 6), (3, 1), ..., (3, 6), (4, 1), ..., (4, 6), (5, 1), ..., (5, 6), (6, 1), ..., (6, 6)}.

I think that for the expected value of Y, E(Y), you add together the larger number in all 36 pairs, and divide by the number of pairs, which is 36. For the 6 pairs that have the same value, pick either number to be the larger; it's certainly not the smaller of the two.