00:01
So in this question we're asked, what percentage of area is between the mean and the rightmost end of the curve? and really, well, you haven't included the curve, so the answer is it depends on the curve.
00:36
But we can go into a little bit what this means.
00:39
So the mean is the expected value.
00:43
Of x and if we have a curve, so take a curve f of x, then the expected value of x is the integral from minus infinity to infinity are f of x times x dx, and then the area that you're looking at area is the integral from the expected value of x up to infinity of f of x dx.
01:20
So we need to work out what this means.
01:25
So basically there's a, this is the most general way of formulating it.
01:36
So this is the most general formulation.
01:44
But what we might have is that, so special cases, we can think about a special case.
01:53
So a special case could be if we have symmetry around the mean, in which case we would have f of x plus the expectation of x is f of the expectation of x minus x.
02:16
And then if we add x to both sides, then, well, if we take away the expectation of x to both sides, then we get f of twice the expectation of x plus x plus x, actually...
02:36
So now let's try and look at what a is in that case.
02:41
So now a is the integral from the expected value of x up to infinity, f of x, dx.
02:47
And now let's make a substitution, y equals x minus the expected value of x...