00:01
You know, this problem we've been given the following probability distribution.
00:03
And we'd like to find the marginal distribution.
00:06
Now to find the marginal distribution for x, we need to integrate out the y.
00:12
So we integrate out from 0 to 1, x plus y, d .y.
00:18
And so this gives us x, y, plus 1ā2, y squared, evaluated from y is 0 to 1.
00:27
And so this is x plus 1ā2.
00:34
And so our marginal distribution for x is x plus 1ā2.
00:39
With x going from zero.
00:45
Now for a marginal distribution for y, notice that this is just going to be the exact same thing, because you do the exact same integral.
00:52
And so similarly, we have f of y is y plus a half.
00:59
Now in b, we want to find the probability that x is bigger than 0 .25 and y is greater than a half.
01:13
And so here we need to integrate...
