00:01
So in this question we have b and c are both uniformly distributed on the interval 0 to 1.
00:08
So that means that the density functions are going to just be 1 for when they're in that interval and 0 otherwise.
00:23
And the same for fc of c.
00:29
So first of all, we want to calculate the expectation value of b to the n.
00:34
Well, that's going to be the integral from 0 to 1, b to the n.
00:39
Times 1 db, which is 1 over n plus 1, b to the n plus 1, evaluated between 0 and 1, which is just 1 over n plus 1.
00:55
So now let's get the variance of b to the n.
00:58
Well, the expectation of b to the n squared is the expectation of b to the 2n, which is 1 over 2n plus 1.
01:10
So the variance of b to the n is the expectation of b to the n squared minus the expectation of b to the n squared, which is 1 over 2 n plus 1, minus 1, minus 1, minus 1, minus 1, minus 1 over 2n minus 1, n plus 1, over 2n plus 1, n plus 1.
01:35
Oh, this has to be squared.
01:44
So this is going to be n plus 1 squared.
01:46
That's going to be n plus 1 squared down there...