00:01
For this problem, we are told that a red dye and a green dye are rolled, and the random variable x is the larger of the two numbers facing up.
00:08
We are first asked to give the probability distribution for the indicated random variable.
00:12
To do that, we will need to start out by indicating our sample space.
00:16
So this is the sort of standard for dice, as has been seen in a few problems by this point, but i'll write it as row by row, giving the result in the first, or for the first die.
00:27
We can say that it's for the red one.
00:30
And column by column is the result in the green dye.
00:33
So we have 1 -1 -1 -2 up to 1 -6.
00:37
Then 6 -1, or excuse me, not 6 -1.
00:40
We want 2 -1 there.
00:44
So we have 2 -1 -2 -up to 2 -6.
00:49
Then i'll just project this downwards here.
00:52
We'd have 6 -1 through to 6 -6.
00:58
Then we can see that the random variable x, corresponding to each, each outcome in the sample space would be 1, 2, up to 6.
01:10
Then we'd have 2, 2, 2, up to 6.
01:14
Or actually i'll specify 2, 2, 3, 2, 3, up to 6.
01:17
Then we'd have 3, 3, 3, 3, up to 6, 4, 4, 4, 4, up to 6.
01:30
And actually, i won't this far along, i'll write this out explicitly.
01:34
We have 5, 5, 5, 5, 6, and lastly, a row entirely of 6...